Will a deep-blue state elect another Republican governor to succeed Larry Hogan? Tuesday’s competitive primaries will signal where the race is headed.SILVER SPRING, Md. — Tuesday’s primary elections for Maryland governor come at a moment when Democrats are jittery, unsure of the future and perhaps willing to bet on a flashy, unproven commodity.That could be a real problem for Tom Perez.As he did in early 2017, when he won a contest among party insiders at the dawn of the Trump era to become chairman of the Democratic National Committee, Mr. Perez is pitching himself as the safe establishment choice.But polling in the Democratic race for governor shows a dead heat between Mr. Perez and Wes Moore, a best-selling author, television show host and nonprofit executive who has been endorsed by Oprah Winfrey. Peter Franchot, the state comptroller and a fixture of Maryland politics since the 1980s, is close behind.The race, like Maryland’s Republican primary for governor, will test voters’ appetites for competence and experience at a time when the bases of both parties are angry at their political establishments.Republicans will choose between Kelly Schulz, a former cabinet secretary for the departing Gov. Larry Hogan, who is term-limited, and Dan Cox, a first-term state delegate who has been endorsed by former President Donald J. Trump and who wrote on Twitter during the Jan. 6, 2021, attack on the Capitol that Vice President Mike Pence was a traitor.Mr. Cox is also one in a string of Republicans who have received help this year from Democrats pursuing the hazardous strategy of trying to elevate far-right G.O.P. primary candidates in the hope that they are too extreme to win a general election. The Democratic Governors Association has spent $1.16 million on advertising trying to lift his candidacy — more than all the Republicans combined have spent on TV and radio ads, according to AdImpact, a media tracking firm.While the Republican primary is a battle between Mr. Hogan’s center-right political operation and Mr. Trump’s far-right supporters, the Democratic primary has developed as a stylistic contest with few ideological differences: Mr. Perez’s awkward-dad competence, Mr. Moore’s charismatic dynamism and Mr. Franchot’s decades of experience in state politics.Wes Moore, a best-selling author, television show host and nonprofit executive, has faced questions about elements of his personal story.Sarahbeth Maney/The New York TimesDemocrats are eager to win back the governorship of a deep-blue state that has been led by a Republican, Mr. Hogan, since 2015. At the same time, Democrats hold veto-proof majorities in both chambers of Maryland’s General Assembly that are likely to withstand even a strong Republican showing in November thanks to the state’s gerrymandered districts.Neither party’s primary has garnered the nine-figure sums spent on television and radio advertising in other states’ races. Mr. Perez and a super PAC supporting him have combined to spend $3.5 million — more than any other candidate in the governor’s race.Mr. Perez has highlighted his years working in the Justice Department and as labor secretary under former President Barack Obama. In his TV ads — one of which uses Mr. Obama’s voice promoting Mr. Perez — he describes himself as the candidate from the “get stuff done” wing of the party, though he uses a more pungent noun than “stuff.”In an interview on Thursday at an early-voting site in Silver Spring, an inside-the-Beltway suburb, Mr. Perez said Democrats would be taking a big risk in the general election if they nominated Mr. Moore.“I’ve been Senate-confirmed twice,” Mr. Perez said. “I’ve run for office twice. I’ve been vetted for vice president in 2016. I won’t spend the general-election campaign explaining something that I did in the past or that I didn’t do in the past.”Mr. Perez was referring to the fact that elements of Mr. Moore’s inspiring personal story have been challenged.A Rhodes scholar and a veteran of the Afghanistan war, Mr. Moore has placed his biography at the center of his campaign. He wrote a best-selling book that was promoted by Ms. Winfrey, who later gave him a show on her cable channel.Mr. Moore has repeatedly described himself as a Baltimore native, but he was born in the Washington suburbs and raised in the Bronx; he did not live in Baltimore until he enrolled at Johns Hopkins University.And he has sometimes not corrected interviewers who made flattering mistakes about his résumé, including one who said he had been inducted into a Maryland hall of fame for football (an institution that does not exist) and at least two others who described him as a Bronze Star recipient (he is not).Brian Jones, an aide to Mr. Moore, said the candidate had never given any false impressions about his record. He declined requests to make Mr. Moore available for an interview.“Wes Moore has absolutely nothing to exaggerate, he has absolutely nothing to regret, and anyone suggesting otherwise should be ashamed of themselves,” Mr. Jones said.Mr. Moore at the Robin Hood Foundation’s 2018 benefit in New York. He earned nearly $1 million a year at the organization.Krista Schlueter for The New York TimesMr. Moore’s most recent job was chief executive of the Robin Hood Foundation, an anti-poverty organization in New York where he was paid nearly $1 million a year.There, in 2018, questions were raised about the amount of overtime Mr. Moore’s executive assistant was accumulating. The assistant, Maria Flynn, wrote a memo, reviewed by The New York Times, stating that Mr. Moore had “required” her to perform a litany of personal tasks for him, including booking Amtrak tickets for Mr. Moore’s nanny and scheduling, negotiating and drafting contracts for his many paid speaking engagements.Ms. Flynn was fired a week after submitting her memo.Robin Hood investigated Ms. Flynn’s allegations. According to an internal report reviewed by The Times, Mr. Moore told Robin Hood that he had asked Ms. Flynn not to submit for overtime pay for personal work she did for him outside the hours she worked for the organization and had instead “personally compensated” her with an unspecified quarterly bonus.The investigation ultimately concluded that Ms. Flynn’s termination was justified because she had filed excessive overtime hours with Robin Hood and had improperly “migrated files to her personal email account.”A separation contract she signed stipulated that Robin Hood would pay her $23,925 — three months’ pay and benefits — if she agreed not to sue the group or speak ill of her experience working there for Mr. Moore.Ms. Flynn said she could not discuss her tenure working for Mr. Moore because she signed a nondisclosure agreement upon her dismissal.“I didn’t have the money to hire a lawyer,” she said. “I wasn’t able to fight.”A Robin Hood spokesman, Kevin F. Thompson, declined to discuss Ms. Flynn’s specific claims or the internal documents.“We take all employee misconduct allegations seriously, and we never had cause to take any disciplinary actions against Wes Moore,” he said.Mr. Jones, the aide to Mr. Moore, said the claims in Ms. Flynn’s memo were false and said they had surfaced through “flimsy opposition research” by Mr. Moore’s political opponents.The third major candidate in the Democratic primary, Mr. Franchot, said in an interview on Friday that his long career in Maryland politics would be valuable in addressing voters’ concerns about inflation and high gas prices.“People are looking for a steady hand at the helm, somebody that has had experience, obviously knowledgeable about the state’s economy,” said Mr. Franchot, who was first elected comptroller in 2006 and served in the General Assembly for two decades before that. “I’m the person that’s been on the stage for the last 16 years.”Republican voters face a different type of decision — whether fealty to Mr. Trump and lies about the 2020 election carry more political weight than Mr. Hogan, a two-term governor who cast himself as a check against excesses of Democratic supermajorities.Ms. Schulz, a former state delegate who spent nearly seven years in Mr. Hogan’s cabinet, has adopted the governor’s mantra and is betting on their political alliance. She would most likely be a formidable candidate in the general election. Mr. Hogan remains one of the nation’s most popular governors, and while the state has more than twice as many registered Democrats as Republicans, it has elected only one Democrat, Martin O’Malley, as governor since the turn of the millennium.Kelly Schulz held a baby in front of cutouts of Democratic politicians at an event this month in Annapolis. She has pitched herself as a moderate Republican successor to Gov. Larry Hogan.Matt Roth for The New York Times“She understands the nuance of what you have to do to win as a Republican in Maryland,” said Mileah Kromer, a pollster at Goucher College in Towson, Md.Ms. Schulz predicted that Mr. Cox would lose the general election by 30 percentage points to any of the Democrats running.“I don’t think there’s a single person out there in the state of Maryland that actually believes that Dan Cox can beat a Democrat in November,” she said in an interview, calling Mr. Cox an “out-of-control conspiracy-theorist-type person.”Mr. Cox’s campaign manager, his daughter Patience Faith Cox, did not respond to requests for comment.The Democratic Governors Association agrees with Ms. Schulz’s assessment. It has essentially fueled Mr. Cox’s entire ad campaign. Mr. Cox has spent just $21,000 on television and radio ads, yet polls show him tied with or leading Ms. Schulz.Mr. Cox has been a prolific amplifier of pro-Trump conspiracy theories about the 2020 election. In December 2020, he wrote on Facebook that Mr. Trump should use the federal government to “seize federal vote machines in states where fraud is exceedingly rampant.”He chartered three buses from his home base in Frederick County to the Jan. 6, 2021, rally to protest the election results. That day, after the mob had breached the Capitol amid chants of “Hang Mike Pence,” Mr. Cox tweeted, “Pence is a traitor.”Dan Cox, a Republican state delegate in Maryland, has been a prolific amplifier of pro-Trump conspiracy theories about the 2020 election. Brian Witte/Associated PressAhead of Tuesday’s primary, Mr. Cox has threatened lawsuits seeking to invalidate mail-in ballots and warned without evidence that “there have been mules in Maryland” illegally stuffing ballot drop boxes, a reference to a Trump-promoted film that makes false claims about voter fraud in the 2020 election.The counting of absentee ballots is expected to last for days after Tuesday’s vote. Maryland law forbids the processing and counting of ballots returned in drop boxes or by mail until Thursday, and aides for several candidates have warned that the winners in each primary may not be known until late in the week.Delegate Ric Metzgar, a Republican who is backing Mr. Cox, said that Mr. Hogan had alienated the party’s base by breaking with Mr. Trump and that Ms. Schulz had failed to present herself as anything beyond an extension of Mr. Hogan’s administration.“There’s not many Republicans supporting him at this moment, he’s distanced himself so far away from Trump,” Mr. Metzgar said. “You can’t ride coattails if there’s no coattails to hang on to.” More