I dont know if there is any one Supreme Court Case that says that. The classic case enunciating the principle that the police are under no affirmative duty to protect citizens is Riss v. New York, 27 N.Y.2d 579, 240 N.E.2d 860 (N.Y. 1968). You can search for this case and also search for other cases that have cited it.
In Riss a woman attempted to sue the city of New York after her ex-lover hired a man to throw lye in her face on the street. She was blinded in one eye, partially blinded in another and suffered serious scars.
It seems the guy had told her he was going to have it done and she, in turn, had reported it to the police on multiple occasions and requested protection. The police, however, did nothing about it and, as I stated above, she ended up suffering serious injuries. She sued the city in tort (on a negligence theory) only to have the suit dismissed at summary judgement - the court found that the police had no duty to Ms. Riss to protect her. In the world of the law, if you dont have a duty to someone you cant be neglgent towards them - hence, no case. The NY appeals courts upheld the decision.
The basic tort principle that you cant sue the police for not protecting you is pretty much bed rock legal principle enshrined in the common law and statutory of just about every state (there are exceptions and variations from place to place in the specifics of it all). In fact, its still taught as "black letter law" to first year law students at law school around the country.
By the way, the book "stopping power" has a great section on this and cites some ordinaces and statutes as well as case law.
By way of disclaimer: I'm not a lawyer, so dont take what I say on the law as authoritative.
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"If a man neglects to enforce his rights, he cannot complain if, after a while, the law follows his example. . ." - Oliver Wendell Holmes
