Thanks to the circumstance of having a camera that watched the street in front of 506 East 13th Street, Ms. Millstone could provide investigators with a video that pierced a fog of evasions and fictions created by the two officers about the hours after midnight on Dec. 7, 2008. The recordings documented that they had gone into the woman’s building at times when they had claimed to be elsewhere.

Without the tape, prosecutors said, the case would have been virtually impossible.

It showed that around 1 a.m., a woman was escorted into the building by two police officers, Kenneth Moreno and Franklin Mata. They had been called there by a cabdriver who sought help getting the woman out of his taxi.

The next morning, the woman, 29, testified, she woke up naked except for a bra, in a puddle of vomit, and believing that she had been raped the night before by a police officer. She testified that she took a shower and then went to the apartment of friends in the building. They took her to the hospital.

That morning, two other friends went to Heather’s, and asked Ms. Millstone if her doorman had seen anything unusual the night before. Ms. Millstone told them about the surveillance camera. They began to log the events on the tape.

The police officers escorted the woman into the building at 1:10 a.m., and left seven minutes later. They returned at 1:52 a.m. and left in 17 minutes. Their next visit was around 3 a.m. and lasted 33 minutes. They last were seen entering at 4:27 a.m., and leaving at 5:07 a.m. In all, they spent about 97 minutes in the woman’s building.