I used to work in law enforcement, and can speak to this from my experience.
First of all, there are departmental regulations. In the course of our jobs (I worked for a District Attorney's office) we had access to all kinds of information on all kinds of people. Their vehicle and driving records, their criminal histories, court records, the information that employers, banks and securities firms report to social security and to income tax, copies of their actual tax returns, real property records, we could even use local post men to tell us what names were receiving mail at what addresses. (Yes, the post office tells the police that and we often asked for that information.) That's just stuff available on request, without a subpoena. We had access to that kind of information for many celebrities.
We were told that if we EVER used any of that information for ANY purpose not directly related to a case, it would mean termination and if appropriate, criminal prosecution. They weren't fooling around either and it wasn't a hollow threat. Everybody who worked there knew that. That's where I think that this police officer might be most vulnerable. Even if he just remembered her address from seeing her driver's license at the traffic stop, if he saw that license in the course of his official duties, then these kind of regulations would apply.