Probably not, of by killing yourself you mean just "switching off".
The autonomous nervous system (the parts that control your breathing and heartbeat for example) are automatic, and require no input to function from a conscious mind. Clinically brain dead patients, for example, have no higher order brain functions or subconscious ones, but can still be kept alive so long as they have a respirator; their hearts will continue to beat so long as oxygen is present.
Now, if you want to think of a very bizarre hypothetical, it could be possible to 'murder' yourself if one had Alien Hand Syndrome, and the rogue arm wished harm upon you and access to a weapon.