A traffic citation is the equivalent of a complaint filed in court, the stop is a detention (arrest).
Signing the citation is nothing more than a personal recognizance bond, it is a promise to appear. It is not an admission of guilt, rather it is acknowledgement that you are aware of the charges against you (not that you agree with them).
If you refuse to sign, many states REQUIRE that you appear IMMEDIATELY before a magistrate, which means you get placed in the back of the cruiser, in handcuffs (you are under arrest) and your vehicle needs to be dealt with. If there is no one immediately available to take custody of the vehicle, then it is towed, as it can not be left at the side of the road.
Guess who pays the towing fee? (hint- not the PD)
Guess what happens if the magistrate is not in at the time? (another hint- you are NOT released)
Guess what happens when you see the magistrate? They will confirm your court date and the charges against you and give you a PR bond, which you MUST sign before you will be released. (some courts may take your plea at the time)
Sign the citation and fight it in court.