If you live in one state and have a doctor in another (because they don't offer the treatment to you, unless you're a pregnant female), can the police in your town call your doctor and tell them not to prescribe people from your town - when you did nothing wrong at all.
Only the courts have legal authority to order a licensed medical practitioner to refrain from writing a legal prescription, or to order a licensed pharmacist to not fill one. I assume that is what you mean by "tell him not prescribe people from our town". Additionally, the courts of one state only have jurisdiction over actions in that state, so an Idaho judge cannot restrain a doctor's practice in Washington. The fact that a customer is an Idaho resident does not change that.
Police can give orders in furtherance of their official duties. Generally, that relates to immediate situations, such as an order to sit on the ground (during an arrest), step aside (when executing a search warrant), and the like. It depends on the state, but many states have "emergency powers" laws that allow the governor to give orders (such as evacuation) as are felt to be required in an emergency, and that authority may be transmitted to local police. If the governor (of that state) issued such an order, then police of the other state could enforce it (but that hasn't happened).
If an officer felt that the people from one town were selling oxycodone, he might feel that as a citizen, he should try to persuade the local doctor to stop writing those prescriptions. Persuasion is always legal; going beyond persuasion (acting under color of law) requires legal authority, which would be lacking in the situation you describe.