I suppose someone of Mike's men actually killed the girl and let senator Geary think the killer was himself, while they arrange to have things mended and gain Geary's obedience because he'd feel in debt with Mike.

BTW, in my opinion senator Geary is one of the WORST character of GF, right?

I don't want realism. I want magic! Yes, yes, magic. I try to give that to people. I do misrepresent things. I don't tell the truth. I tell what ought to be truth (Blanche/A streetcar named desire)