this is untrue (albeit somewhat arguable, and varies from state to state)
For the most part, cops cannot and will not ever "commandeer" your vehicle. Most states include a clause within their respective constitutions that states something along the lines of : "if a law enforcement official requests assistance; you must comply or face a fine" (usually $500-$1000).
The purpose of this clause isn't so police can take your car or tell you to tackle a fleeing criminal, but rather a safeguard to prevent friends and/or family of criminals from harboring or assisting the criminal by interfering with the police, that isn't covered in the "harboring" or "interference" clauses. It also helps prevent idiots who don't know the criminal from interfering without knowing it. Example: a criminal is spotted entering a restaurant to lay low, and is hiding out in the bathroom for a while (this actually happens alot). The police show up and ask the hostess where the bathrooms are and asks if they've seen anybody. The hostess says "There's a 45 minute wait sir" because she doesn't like the police because she listens to rap. Legally she must comply with the officer's wish to know where the bathrooms are because of this clause, due to the fact she's neither harboring/interfering. This is one example of many statutes that are in place to "patch" specific circumstances like this, and every state has their own version of this statute.
I have never once heard of a case (outside of tv) where a police officer taking a civilian vehicle occurred. If it did occur, I would assume the officer/department would be sued heavily and likely face criminal action, although it would bring into question the semantics of that state's statute regarding the "assistance" clause.
Long winded response but I thought I would provide some insight to help educate people against hollywood myths. If a cop asks to borrow your car to pursue a criminal, say no and ask for the cop's name/dept/DSN.