Most Helpful Guy
Murder. The gun is in the wrong hand to make the impact splatter, the cig is half smoked with no attempt to put it out, so out would've been an awkward way to kill yourself and the stain would've been elsewhere. Also the pen and the glasses were put down in the middle of writing the letter so who ever it was the victim knew them. The victim seems to be a woman and women rarely shoot themselves in the head, usually in the heart but most by poison.
Most Helpful Girl
Murder : if I was a suicide it's practically impossible that she would still be holding the gun because of the impact. Therefore, the killer must have placed it in her hand to disguise his murder as a suicide.
Plus, we can see she is left handed : the position of the pen, the soda can and the cigarette can tell us that. So why would she hold a gun in her right hand?