In New Hampshire, it's 'Director.'
Autopsies are handled by the medical examiner, who is a certified medical doctor, who has specialized in autopsies and forensic medicine. (Note that this was not always the case. Further note that signing a death certificate can be done by any medical doctor.) The medical examiner can be very different from the coroner. The medical examiner is going to be affiliated with a hospital and have his/her offices and facilities there.
The medical examiner is not responsible to the police department and is independent from the police. The reason is because the medical examiner should form an unbiased cause of death and not be easily pressured into certain results. (This doesn't always work out in practice.)
Samples from the autopsy may be sent to the state lab for further examination, especially for poisons and other toxins. Other samples can be sent to labs that specialize in the testing.
Best of luck,
Jim Clark-Dawe