I guess the doctor lied to me then. He practically swore that he would only speak to me first about the results.
Well, the police cannot force him to speak to them absent a court order. So, he really didn't lie. But, the police can ASK him anything they want. He just doesn't necessarily have to answer them.
Of course, if you want any hope of a criminal investigation, they will have to have access to him or there will be zero chance of any such investigation.
And that he would not be allowed to speak to until talking to me about results. Are you sure it's legal for police to contact doctor while I'm waiting for results? There was a suspicious gash on his head that police did not see when they ruled it natural and missing bank card and money.
A "suspicious gash" can be anything. I'm not going to speculate, because I was not there. But, a fall can create a gash, and the fact that he may not have had a bank card or money on him could be from reasons other than a robbery.
Was an autopsy done at the outset? Was he under a doctor's care for any illness? While the laws vary by state, in general, if someone dies and there is no physician willing to sign a death certificate (i.e. to assert that the death was from natural causes or as a result of an illness for which he was being treated), then an autopsy is usually automatic.