What to do when Mother dies at home?

When my Dad died at home in 2009, all we did was call the funeral home. Dad had been sent home from the hospital on hospice as he was not expected to live longer than 6 months. When he passed, Mom and I were with him. I called the funeral home, but asked them not to come until later in the afternoon, so as to give family members time to come to the house and pay their last respects, and it all worked out smoothly.

Mom's situation may be quite different. She's at home -- I'm caregiving -- and she is slowly going downhill with end-stage kidney failure and CHF. A couple of days ago she developed pneumonia, which thankfully I caught really early -- the doctor confirmed pneumonia but said it was "slight" and prescribed 5 days of antibiotic. Still, even "slight" pneumonia has her feeling exhausted and worn out, and her appetite has dropped off a bit. She hasn't been put on hospice yet, and so far I'm able to help her with all that needs doing.

My question is this: if she passes suddenly here at home, without yet having been put on hospice, can I still simply call the funeral home as I did with Dad, or would I need to call the police or someone else first?