What determines state residency when it comes to health insurance?

I live in New York but also rent an apartment in Connecticut. I am not a signatory on the lease (I rent a room in a friend's apartment), but sometimes stay there for work. The premiums for health insurance are much lower in Connecticut than they are in New York, and I was wondering if I could sign up for health insurance there. I know I would only be covered in Connecticut. Is this something I could do and if so, what kind of documentation would I need to provide to prove my Connecticut residency? Thanks
--------------------
It's likely the state in which you file your taxes. Home state It would follow that rule.
Source