My mothers tv was stolen, I reported this to administration and filed a police report. Who's responsible for replacing or reimbursement of this?

I personally would hold the NH responsible (but read the admission agreement). Assume it was a table top model? I think it would take quite some time to disassemble a wall mounted unit without someone noticing. You could also demand a search of all the other rooms in the NH (or just walk around and peek in yourself to see if you can spot it). Sometimes other residents walk into other rooms and just help themselves to whatever appeals to them (due to their dementia). Other than that, if your Mom still owns her home/condo/apt., and has a HO/tenant's ins policy, there may be coverage for this stolen item even if it is currently placed in the NH.