In episode 2, Mare seemed to think that it was from a gun shot. When she talks to the chief at the crime scene, she makes a finger gun gesture to explain the wound to the head.
This is from @SnazzyDaisy's post in the "Fathers" episode thread:
Whether the wound looks like it's from a gun is debatable, but the Easttown police believe it to be. The show has been coy about confirming cause of death. You would think that the Medical Examiner scene would confirm the cause, but it doesn't. So with nothing to refute Mare's initial hypothesis, I am assuming Mare's cause of d