If you are a Hawaii nonresident, and you have no Hawaii-sourced income, then no, you probably will not have to file a Hawaii income tax return. An interesting fact about military servicemembers stationed in Hawaii - even though they are stationed here, as long as they claim another state as their "state of legal residency", their military income is not considered to be "Hawaii-sourced", and therefore will not be subject to Hawaii income tax. Because of this, many military servicemembers often get used to not having to file Hawaii income tax returns.
But if a military servicemember is pcs'd out of the state, and turns their Hawaii home into a rental, different rules apply. Even if the servicemember continues to claim another state as their resident state, they still need to file a Hawaii tax return. Here's what the instructions for the Hawaii N-15 (nonresident or part-year resident tax return) says:
Every individual doing business in Hawaii during the taxable year must file a return, whether or not the individual derives any taxable income from that business. “Doing business” includes all activities engaged in or caused to be engaged in with the object of gain or economic benefit, direct or indirect, except personal services performed as an employee under the direction and control of an employer. For example, every person receiving rents from property owned in Hawaii is “doing business” and must file a return whether or not the person’s expenses exceed the gross rental income.
When taxpayers file for a HARPTA refund, one of the first things the reviewer does is to check to ensure that all required tax returns were filed, and all taxes paid. So it's important that home sellers who are subject to HARPTA stay current with all of their tax filings. General Excise Tax. Transient Accommodations Tax (if required). And lastly, Hawaii income tax returns for the years you operated the rental.