I haven't taken family law. Your guess is as good as mine. I'll give you my guess anyway, though. I have absolutely no idea whether there's any chance of criminal charges here. That would depend entirely on the laws in Wichita, Kansas, I suppose. Civilly I suppose we'd be looking at a potential negligence claim. Typically a person has no legal duty to help another unless the would-be rescuer created the person's danger. The classic example is that an Olympic swimmer can sit by a swimming pool and smoke a cigarette while he watches a person drown. He has no duty to help the drowning person, no matter how good a position he was in to provide help.
There are exceptions to this rule, however. People with special relationships can have affirmative duties to provide reasonable care and protection. The category of special relationships that I could see being relevant here is custodial relationships. People with custodial care over another person may have a special relationship giving rise to an affirmative duty of care. You might say that this guy had a custodial relationship with this lady, but it seems like that would be a hard sell. The lady is an adult who chose to be there. For example, while schools K-12 usually have a special relationship with their students, universities usually do not. The primary reason for this is that the latter is dealing with adults who chose to attend school.
Another theory that might get him is the undertaking doctrine, which says that once you've undertaken to help someone, even where you had no duty to do so, you assume a duty of reasonable care. One might argue that by keeping her fed and so on, he was under a duty to act with reasonable care. If a judge found that he did have such a duty, his case could then go to a jury to decide whether notifying authorities falls within the scope of "reasonable care".
Keep in mind that I am in my first year of law school . . . this is just the first stuff that comes to mind. I'd have to research actual case law to give you a good answer. While I have unlimited access to the normally retardedly expensive tools to conduct such research, I don't have anything like an inclination to spend a lot of time on this.