LOS ANGELES — Authorities investigating allegations of rape against a Los Angeles police officer discovered evidence through DNA testing that he had committed a second, earlier sexual assault, police said Wednesday.

The officer, William Rodriguez, 33, a 10-year veteran of the police department who was assigned to the traffic division in the San Fernando Valley, was arrested Tuesday on two counts of forcible rape, with a special allegation of multiple victims, in connection with a report of a sexual assault last November, the Los Angeles County District Attorney's Office said.

Police said that when they ran Rodriguez's DNA through the FBI's Combined DNA Index System, they got a "hit" on a cold case from August 2015. Prosecutors said that assault involved another female victim who was raped under similar circumstances.

Police said Rodriguez, who was in custody and had been relieved of his police authority, was off-duty at the times of the alleged assaults.

Rodriguez was being held pending an arraignment Thursday. Prosecutors said they would seek bail of $1.2 million on the charges, which carry a maximum sentence of 30 years to life in prison.

"When one of our own breaks the trust of the people we are sworn to protect and to serve, it tarnishes the badge we all wear proudly on our chests," Police Chief Michel Moore said in a statement. "This arrest also reflects our commitment to pursue every lead no matter where the investigation takes us."