For me when I took my placenta home from the hospital, I had it stored in a plastic container with a label on it that was just like my ID badge. It was then put in a plastic bag so it was easy to carry, and then we kept it into the fridge until
we left(which would have been only about 4 hours or so after giving birth, but we decided to stay 24).
There were no questions asked, and it was actually recommended to me by my midwives to take it home and bury it. I had originally only wanted to see it, but after seeing it and discussing it with my husband and midwife, I wanted to take it home