You must not understand the law. Eastwood gives the lethal injection. That is administering death, i.e. euthanasia. It would have been assisted suicide if Maggie did the deed herself. Here is the transcript for proof of what occured in the film:
[Hospital lobby]
Nurse says she is going to get a cup of coffee.
[Frankie enters Maggie's room. Maggie is awake, seemingly no longer sedated]
Frankie: all right. I'm going to disconnect your air machine and you're going to go to sleep. Then I'll give you a shot, and you'll stay asleep. [Gaelic phrase] means "my darling, my blood."
[Single tear leaves Maggie's right eye]
[Frankie gives her the shot, piano starts up.]
Narrator: He gave her a single shot. There was enough adrenaline to do the job a few times over. He didn't want her going through this again. [Piano] [then violins] Then he walked out, I don't think he had anything left. Marta --