For most people, the answer is no. What matters is where you earned the income—not where your employer is located.
If your employer is based in Arkansas, Connecticut, Delaware, Massachusetts, Nebraska, New York, or Pennsylvania, you must pay income taxes where your employer’s office is located.
Example 1: Charlie is a Vermont resident working in Michigan, where their employer is located. They would file a nonresident Michigan return in addition to their resident Vermont return. However, if they're working remotely in Vermont for a Michigan employer, they'd only file a resident return for Vermont, which is where they earned the money.
Example 2: Blake works from home in New Hampshire, but is employed by a company in Connecticut. They have to pay Connecticut income taxes under the convenience of the employer rule, even though their home state of New Hampshire doesn’t have income tax.
Since payroll departments aren't always aware of how withholding works, remote employers sometimes withhold taxes for their state, not the employee's state.
In these cases, you need to file a nonresident return to recover the erroneous withholdings. On the nonresident return, declare earnings of $0 so you can get a full refund for the taxes your employer withheld. You should also tell your payroll department so they fix this in the future.