SAN JOSE — The woman who prosecutors contend was raped by an on-duty San Jose police officer reported the sexual assault only after being arrested three weeks later on suspicion of drunken driving, this newspaper has learned.

Prosecutors don’t dispute that the arrest by the CHP may have been the catalyst that drove the woman to report the alleged rape by an officer from a different agency. But they note that the case against the cop is supported by DNA and other evidence.

Even so, the timing of the woman’s accusation against Officer Geoffrey Graves is likely to become a central issue in the case, experts say. The defense may seek to discredit the woman, suggesting she tried to barter her way out of her own legal predicament by implicating the officer. Her arrest also may bolster a possible defense claim that she has a drinking problem and is therefore unreliable.

But prosecutors are well prepared to make their case. In addition to DNA evidence bolstering the sexual assault charge, prosecutors say, the woman never requested leniency in exchange for reporting the San Jose officer. And court records show she pleaded no contest and received a typical sentence for a first conviction of driving under the influence of alcohol.

“Any notion that this report was made to avoid a DUI conviction is absurd,” said Carlos Vega, the prosecutor in charge of the rape case. He noted that the misdemeanor DUI case was handled independently by a different prosecutor.

Regardless of how the DUI arrest figures in the cop case, it helps resolve a lingering question: What occurred to prompt the woman, who is in the country illegally, to risk deportation and level the explosive accusations?

Graves, who is free on $100,000 bail and on paid administrative leave, could not be reached for comment. He faces up to eight years in prison if he is convicted. His attorneys did not respond to several requests for comment.

The charges against the officer, whose department has struggled to build trust with the city’s immigrant communities, stem from a Sept. 22 family disturbance call.

Graves was one of four officers responding to an argument between the woman and her husband. The officers noted that the couple had been drinking — an observation that may now take on more importance.

Graves and another officer traveled to a hotel and waited for the woman to check into a room so she and her husband could spend the night apart. After the second officer left to answer another police call, Graves allegedly stuck around and later returned to the woman’s room, where he overpowered her and “forcibly engaged in sexual intercourse with the victim before leaving the hotel approximately 10 minutes later,” according to a San Jose police report.

Twenty-one days later, on Oct. 13, two CHP officers on patrol near Moorpark and Leigh avenues pulled the woman over after she ran a red light in a green minivan and weaved across lanes, according to court documents.

The woman became extremely agitated and demanded in broken English to be let go. Her blood-alcohol level was 0.15, nearly twice the legal limit, according to CHP reports.

Apparently terrified of being sexually assaulted again by officers, she waited until she was in the safety of the Main Jail to report the Sept. 22 alleged rape, sources said.

During her first court appearance, on Jan. 22, she pleaded no contest to the DUI charge and was sentenced to three years’ probation, nine days in county jail if she violates probation and eight days on the weekend work program, most likely cleaning up freeways. She also was ordered to pay fines and fees of about $1,900. She has no prior criminal record, according to court documents.

Vega said that rather than being a liability, the DUI charge carried a silver lining in that it may have made the woman more talkative.

“It was a blessing in disguise because it prompted her to report the rape,” Vega said. “An intoxicated person’s words are a sober person’s thoughts.”

Staff writer Robert Salonga contributed to this report. Contact Tracey Kaplan at 408-278-3482. Follow her at Twitter.com/tkaplanreport.