You file a state income tax return in any state that you lived in or worked in for any amount of time during the year. The number of days doesn't matter. You also file a tax return in any state where you have income from a source in that state, such as rental property or sale of any property in that state, or a business in that state. Of course you don't have to file in a state that does not have state income tax, such as Texas. In a few states you have to file if you worked remotely for an employer in that state.
Your health insurance and car insurance do not affect where you have to file a state tax return.
If the situation is complicated, such as having to file in multiple states, having moved more than once, or not being sure which states you have to file in, you might have to consult a tax professional.
