My dad recently passed away, and his house was deeded to me and my sister. There is no equity in it and neither of us want it. Can we just not pay the mortgage and let the mortgage company foreclose on it. The mortgage is in my dad's name. Do we have any responsibility here? In Michigan...

I suggest that whoever is the executor of your father's estate contact the mortgage company and come to an agreement by which they can take back the house without foreclosure, probably some kind of deed in lieu arrangement. Get all the personal items out before the mortgage company is granted possession or if foreclsorue, that is concluded. I suggest consulting a probate and estate atty and a real estate atty.