Depending on your duties outside of flying you might well be required to pay state tax where you are based. You need to talk with a tax accountant. Where the company withholds is actually somewhat meaningless as you can just file a return to get all that money back. Your total time working however might be over 50% in that state.
The exemption to pay taxes on residence vice place of work also only applies to air carriers. Not sure a 135 operation falls under that definition. If it does not than where you reside is irrelevant.