Hi N2g, sorry, I had a long interruption.
I haven't been able to find any confirming references (1) that "hanged" is the required simple past and past participle in execution by hanging, or (2) that "hanged" would be the recommended past in cases of unlawful hanging, such as murder, suicide, or possibly lynching; or in cases of accidental death by hanging, as a dog accidently killed by his leash, etc.
Re my (1), MW Unabridged says "sometimes hanged in the past" for both the transitive and intransitive death by hanging definitions. As I've said previously, American Heritage has a "Usage" section at the end of the entry, and about a third of the "Usage Panel" allows "hung."
Re murder, suicide, and accident: MW gives tr. b(1): to put to death by suspending from a cross, gibbet, or gallows intr. b(1): to die or become dead by hanging (I assume this refers back to tr. b(1).) It seems to me that this would admit murder but exclude suicide and accident.
American Heritage gives tr. 3. to execute by suspending by the neck (to execute tr. 6 to subject to capital punishment) intr. 2. [to hang] to suffer death by hanging (again, I assume this refers back to tr 3.) The "usage" note says, "when the verb is used in the sense of capital punishment etc." IMHO this limits "hanged" to uses involving capital punishment, but sort of by default. No one seems very assertive on the subject.
Best wishes, - A.
Edit. Google: "hung himself" 231,000 "hanged himself" 288,000 (What do they know?)