What is the difference between hand it over to and hand it to

"Hand it over" implies a transfer of ownership, whereas "hand it to" does not necessarily carry that same connotation.

Furthermore, in the case of a police officer telling a person to "hand it over" the statement should probably be interpreted as a command and not a request, and specifically a command for the person to surrender whatever "it" is. In contrast, an officer telling that same person to "hand it to" them would likely be viewed very differently by that person - the statement in this case carries a tone of equality and seems like a request for cooperation much more than a command for surrender.

An air Marshall demanding a airline passenger surrender their pocketknife: "Hand it over."

A detective asking a witness to let him see the possible clue: "Hand it to me."

Edit to reflect the changes to the question:

It is important to emphasize that in practice these two statements could easily be used interchangeably, but if you really want to dig into the semantics there is perhaps a palpable (though subtle) difference in the details. In particular, "hand it over to the police" more strongly conveys the idea of transferring control and / or ownership of a thing (a piece of evidence, a case file, a situation, etc.) out of necessity, while "hand it to the police" sounds like more of a casual statement, or even a non-binding recommendation.

Your boss might tell you to "hand the situation over to the police," while the coworker you asked for advice might recommend that you "hand it to the police."

Beyond the sense of surrendering an object to the custody of someone else (as user251563's useful answer details), there is a complication involving the idiomatic sense of "hand it to." Here is the entry for that phrase in Christine Ammer, American Heritage Dictionary of Idioms (1995):

hand it to Give credit to, congratulate, as in You've got to hand it to her; she knows what she's doing. {c. 1900}

So, for example, a person might say

Community relations may be a problem for law enforcement agencies across the country, but you have to hand it to the police in this town: They have earned an enviable reputation for fairness and neighborhood service.

This usage has nothing to do with relinquishing a physical object to someone, either under compulsion ("I know you have the loot; hand it over") or as a matter of passing the object for inspection or temporary use ("Could you grab that screwdriver over there and hand it to me?").