Where's YC with a startup to catch people who sexually abuse children?
Providing law enforcement with better tools might be a worthwhile geek venture (and given the tools they are sold by megacorps, "better" might not even be hard), but with the existing procurement rules (etc etc) it's probably hard for a startup to enter that market.
Alternative route: Build tools to optimize other public office work, and then use the political process to request that freed money (and headcount) is retargetted to supporting the police ("think of the children!"). While there is still a procurement problem, there might be areas covered in less red tape than police work.