In your case, no. However, this is more complicated than it looks up front.
First, you always file a tax return for your home state that reports all your world-wide income. Sometimes, you may be required to file a non-resident return for one or more other states to pay tax on income that is "sourced" to that state. (Your home state will give you an offsetting credit for taxes paid to another state.)
If you are a self-employed/independent contractor, the "source" of your income is the state where you are physically performing the work. However, California is an exception. If you are an independent contractor working for a client in California, that is considered California-source income even if you never set foot in the state.
If you are a W-2 employee, the source of your income is where you physically performed the work. For example, if you were required to work 1 week per year in Alaska for in-person meetings and training, then about 1/52nd of your income would be considered Alaska-source. However, there is an exception. 7 states may impose income tax if you are remote worker, but working for a company based in that state. The states are Arkansas, Connecticut, Delaware, Massachusetts, Nebraska, New York, and Pennsylvania. If you work for a company based in one of those states, but you work remotely from a different state, your income may still be considered to in-state income for the state where the employer is located. The details vary, so you would have to consider each specific circumstance.
