No.  You file a tax return in your resident state where you live and work regardless of where the company is located.

Example:  Taxpayer works in their home as an employee for Company X.  Taxpayer lives in IN and Company X is located in AL.  Taxpayer files all income with their resident state of PA even if there is training in another state for a short period.  If there was any state tax withholding in error for AL, they would file a return for a full refund with no income taxed to that nonresident state.

State tax law always refers to "domicile" when determining residency.

• An individual may have many residences, or physical dwellings in which he resides, but can have only one domicile, or that permanent residence to which he intends to return. A review of states residency requirements show that 28 states use some definition of domicile to determine if a taxpayer is a resident.