Is my physician allowed to speak with the police about my treatment, or give them my records without a warrant or court order?

No: No, but the laws in your state may be different.

Depends...: If you mean your primary dr, unless certain forms of abuse are suspected, then no. If in the er, it depends on why there--gun shot or stab wounds, fatal car accidents, or similar situations have less privacy rights due to the time sensitive needs of law enforcement, but disclosure is limited.