The two officers had responded to a 911 call from a cab driver, who said the woman was too intoxicated to get into her apartment by herself.
They're accused of taking her to her home and attacking her.
Prosecutors say Moreno then raped her, and Mata acted as a lookout.
Authorities say the two returned to her apartment three times, soon after the initial visit.
The jury selection process started Tuesday after a judge dismissed some misconduct counts against Moreno and Mata .
The officers face up to 25 years in prison if convicted.