Yes, you will need to file an HI nonresident state income tax return to report your HI rental property activities.
According to the HI Department of Revenue, every individual doing business in Hawaii during the taxable year must file a return, whether or not he or she derives any taxable income from that business. Since you are paying a HI GE tax, you are considered to be "doing business" in HI. You will be able to claim these HI GE taxes as a rental expense on Schedule E.
