Why? Just raise the standards. And you can't truly privatize the police because unless you invest them with the power of the state then they're just regular citizens, not bound by the constitutional restrictions of the government. And once you've invested them with the power and liabilities of the state, they're not privatized anymore. It's the exact opposite, it's the state taking over a private company. This isn't like privatizing garbage pick up where the state just indemnifies the private company to conduct a public service. Police powers mean 4th Amendment and other constitutional issues which uniquely bind the government private company. You could privatize the administrative end (non-essential services) but not the street end.
So, it's simpler to just raise the standards. Hire better people. You don't need to privatize for that. Up the pay, up the req's.