No protections occur when private citizens (or companies) give up information to police voluntarily, so the police aren't "searching" anything, in the legal sense of them needing probable cause to obtain information on you.

The only way to stop them from getting anything from Google is to not use Google (and Bing, Yahoo, etc). If Google can tie incognito searches to your name (eg. via IP association), they likely will turn it over in these data requests.

A safe guess would be that Google only hides it from yourself.