In short, based on what you have shared with me, the hospital did have a legal and ethical obligation to notify the police and you, her spouse, that she was leaving. If the reason for her death was the result of an injury that should have been noticed by the hospital, there is also a viable medical malpractice suit as well as they likely breached the applicable standard of care relative to their job duties and responsibilities.
It sounds like, based on what you have shared with me, that there were a series of errors committed by the hospital that, if any of them did not take place, you wife may still be here today.
Their defense will be that she was, in their opinion, was of sound mind to refuse medical care and leave. The entire case will depend on whether or not she was of sufficient sound mind that she could rationally and intelligently sign herself out and be expected to be okay. Since that clearly was not the case by the end result, the burden of proof will be on the hospital to show that something changed that they could not have reasonably foreseen from the time she left, until the time she passed away. That would be hard for them to prove based on the evidence that was present while she was in their care.
Based on what you have shared with me, I think you have a very viable wrongful death law suit against the hospital and providers.
Let me know if you have any other questions or comments. Please also rate my answer positively (4 or 5 stars).
Best wishes and my thoughts and prayers for your loss.