Mueller's lawyer, Gabriel McFarland, has argued in previous hearings that he could be the victim of mistaken identity.
Members of the jury pool also were asked about their experiences with inappropriate touching.
In July, Martinez sanctioned the radio host for destroying evidence.
Baldridge, meanwhile, has said Swift is upset by Mueller's claim that 'for some reason she might have some incentive to actually fabricate this story'.
Swift watched the proceedings closely, occasionally conferring with her counsel.
He says Swift's team told Mueller's bosses at a country music station, and he was sacked from his DJ position.
Dressed in a business-like black jacket and white top, Swift, 27, one of the top-selling US singers, watched the proceedings in a federal courthouse, jotting notes on a pad of paper.
There will be no alternates.
The case has made plenty of headlines even before trial, starting with the photograph of Mueller and Swift that the pop star's legal team wanted sealed - but someone leaked the photo to TMZ.
They must be present for the rest of the trial.
Swift is scheduled to testify.
The questionnaire also asked candidates if they had seen any pictures related to the case - a possible reference to a photo that shows DJ David Mueller with his right hand behind the pop superstar, just below her waist, taken during the alleged offence. Mueller's own suit seeks something along the lines of $150,000 per year of unemployment in damages, though the slander parts of the suit have been previously thrown out by an earlier ruling.
He sued Swift, her mother, Andrea, and her radio promotions director, Frank Bell, in 2015.
Ms. Swift's pretrial deposition provided a preview of her testimony about the events at Pepsi Center, the arena in Denver not far from the courthouse. The disc jockey later sued the singer-songwriter, saying he had been falsely accused and wanted $3 million in damages.
Swift countersued, alleging sexual battery by Mueller. But the prospect of jury selection did not draw many spectators on Monday.
Later, Swift's bodyguard confronted Mueller with the allegation the DJ had reached under the singer's dress and grabbed her. Lorraine Bayard de Volo is expected to offer expert testimony on the ramifications of sexual assault and harassment. Mueller, a morning radio host for Denver's country station KYGO, approached to take a photo with Swift and his then-girlfriend, Shannon Melcher.
Both Taylor Swift and David Mueller are expected to testify in court this week, with the trial looking to last up to two weeks.
Once a jury has been seated, opening statements will take place. Swift might appear. The presiding judge, William J. Martínez, has warned anyone who hopes to attend to refrain from wearing clothing "bearing the name or likeness of any of the parties".