Does my life belong to me, or the State?
False arguement.
The question is "Do I have the right to push the moral burden of ending my life off on another person?"
And the answer is NO!
If you want to kill yourself then do so.
Why are you bringing another person into your decision?
The answer is that they want approval and they want to push the moral burden onto someone else.
If you left a bottle of pain pills beside them they would not overdose.
They crave the drama and they long to have their death be painful for someone BESIDES themselves.
The longer they can string it out and the more high drama they can mix into it the more they like it.
Mostly these are people that are supremely unpleasant and demanding in life. Getting sick does not improve their nature.
Law and Government are supposed to protect your "Life, Liberty and Pursuit of Happiness," and Life comes first both logically and chronologically, since without Life there is no more liberty and no more "pursuit." Thus legal euthanasia perversely undermines the very reason for Law. Similarly, the Medical profession is supposed to protect the patient's health: and nobody is healthier dead.
So go right on ahead and kill yourself (I am speaking sarcastically: please don't to any such thing) --- but above all, don't corrupt me, or your family, or your heirs, or your doctor, or your lawyers, or your lawmakers and government, the major institutions of society, in doing so.
You believe in autonomy? Then be decent and do it autonomously. Ultimately, nobody can stop you making that choice.
God
Neither.