I'm not a lawyer so I can't quote you chapter and verse, But it has been held in court MANY times that the police are not liable to protect you and your family. Many have tried to sue and were told that the police don't even have to respond at all. When you call in an emergency, they may be quick, slow or hardly show at all. You don't know if you are going to get a rookie or a veteran. My daughter is an officer in Texas and she knows of an officer that is just as liable to shoot you as the perp. He is so afraid when making a call he almost always pulls his weapon. He has had several instances where he was suspended for pulling his weapon and threatening people over traffic tickets.
In our minds we have a vision of some superhero coming to our rescue, but the reality is quite different. Each officer weighs the situation as they show up and many would rather just wait it out to see how it goes rather than rush into a gunfight. Today they are in jeopardy as much as the perp if things don't go well. If they do rush to your aid, they may be thought of as a loose cannon or a "cowboy".
IMO, it's best to have a weapon and protect yourself in the first moments of trouble than to mess with cops that may be having a bad day. The police mainly draw the chalk lines and put up the yellow tape.