It depends. States have different rules about taxing employees who moved out-of-state due to the pandemic. We'd have to know specifically which states.
A clue that may help is to look at what's being reported in the state section of your W-2 (boxes 18-20), assuming you told your employer relocated.
If you told your employer you moved and you still had tax withheld from your old state, then you probably have to pay tax in both states. If you have separate state wages and withholding for two states, then you probably can file part-year returns and report only income attributable to each state.
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