Each state has it's own definition ... you did not mention which states are involved.
There is no clear cut definition, as each state has their own requirements. But generally:
- The state where you own or rent property that you live in as your primary residence (with your family if married)
- The state where you are registered to vote.
- The state where you pay property taxes
- The state where your vehicle(s) are registered
- The state that issued you your driver's license.
- The state where your kids (if any) are registered in school and actually attend that school.
- The state where you pay income tax if said state taxes personal income.
Thess are just general guidelines that may not be all inclusive. Each individual state has their own requirements for being considered a resident of that state and not all the above criteria may apply to a specific state.