Would this person go to jail? (Long post)

I'm not sure where else to post this, and this seems like a subreddit where people will have a decent idea.

So this character (J) is 12 years old. He has been severely abused, witnessed his mother's suicide, and seen his brother's drowned corpse. His sister ran away when he was 9, so it is just him and his father.

His father gets drunk and very angry one night so he hits J over the head with a beer bottle before going and grabbing a gun. J manages to run out to the shed and hide from his father, who eventually loses interest and goes back inside.

After a few minutes, J grabs a shovel, goes inside, and slams his father in the head/neck hard enough to severely injure him. He then manages to go back out to the shed and hides under a table.

He is found by the police several days later, still in the same spot. He is starving, dehydrated, and barely conscious.

I am aware that he would likely face legal consquences; my question is if he would go to juvie once he was well enough or if would he go to a mental hospital.

UPDATE: This occurs in a fictional town in Washington. Don't know if that's helpful, but it's probably useful information.

(I have tried to do some research before posting this and am 14, so please keep responses somewhat kind)