Should I file tax return for a state in which I didn't live in 2021?

I moved from MA to WA in Oct 2020 and my employer reported some of my rewards income as MA state income and withheld MA state tax for the same. This is accurate because the bonus amount is calculated for the period from June 2020 to June 2021 and I lived in MA until Oct 2020. Do I need to file state tax as a result of this or should I not? TurboTax doesn't feel I need to file state returns after looking at the W2. @DaveF1006@DanielV01@AmyC