Ah ha! Found it, and it's a pretty long list. Per Wikipedia:
States with filial responsibility lawsAlaska, Arkansas, California, Connecticut, Delaware, Georgia, Indiana, Iowa, Kentucky, Louisiana, Massachusetts, Mississippi, Montana, Nevada (Nevada law only addresses support of children and not support of parents. NRS Chapter 125B), New Hampshire, New Jersey, North Carolina, North Dakota, Ohio, Oregon, Pennsylvania, Rhode Island, South Dakota, Tennessee, Utah, Vermont, Virginia, West Virginia.
https://en.wikipedia.org/wiki/Filial_responsibility_laws