Is there a procedure for filing a final state income tax return?

We are establishing a new legal address this year, 2022 in a state that does not have a state income tax. We will be filing a  tax return for TY2021 for a state that does have a state tax. Do I need to inform that state that this will be our final state tax return? If so are there special forms?

We are both retired, have no jobs. We still own a home in the former state, but will be out of that state for more than 6 months and a day.

Thank you.