The property does not have to be classified as "income property" (it would be property held for investment at best) and you would not have to file income tax returns strictly as a result of holding real property in another state.
Regardless, you should be aware of the SALT limitation.
See https://turbotax.intuit.com/tax-tips/home-ownership/claiming-property-taxes-on-your-tax-return/L6cSL...
