Police maintains the database, so of course they can run a background check. But they don't offer it as a service and don't give away the information to anyone except the person it concerns.
Here in the us I know how insubstantial this claim is. If you know enough law enforcement $10 can get you pictures of a full lookup. And this is with a fairly bare relationship.
So maybe it's not impossible, but it's not something you would do as part of normal HR screening.