If a guy hit me in a casino parking lot and security reported it but they won't give me a copy without warrant or court order, how do I go about getting one?
You need legal process to get it: the casino's internal security's report is not a public record or document and they don't have to release it without some court order or subpoena. You can sue the at-fault driver for your injuries, car damage, costs, etc; once you file that lawsuit, you can issue a subpoeana to the casino and/or its security firm to get the report.
HOWEVER, if this was an Indian or tribal casino, bear in mind that Indian tribes and their casinos are separate legal jurisdictions, and a tribe-owned business on tribal land most likely does not have to honor a subpoena from a state court (though they may voluntarily do so) unless you then bring a separate legal action in tribal court and get that court to order the release. Suing a tribal entity is a lot like suing a foreign business in a different country; it is not something easily done. If it is a tribal casino, unless you are absolutely convinced you need this report, it may not be worth the effort to obtain it.