I've read through section 237-16.5 of the HI state General Excise Tax law at http://files.hawaii.gov/tax/legal/hrs/hrs_237.pdf and can't find anything that definitively exclude out of state rental property owned by a Hawaii resident. But in section 237-16.5(a) which applies to 2018 and earlier, there's a sentence that "insinuates" the GET only applies to rental property physically located in the state of HI. It reads:
(a) This section relates to the leasing of real property by a lessor to a lessee. There is hereby levied, and shall be assessed and collected annually, a privilege tax against persons engaging or continuing within the State in the business of leasing real property to another, equal to four per cent of the gross proceeds or gross income received or derived from the leasing; provided that where real property is subleased by a lessee to a sublessee, the lessee, as provided in this section, shall be allowed a deduction from the amount of gross proceeds or gross income received from its sublease of the real property
Note that I bolded that "within the state" part. To me, that insinuates that since the property is not in the state of HI, then you're not required to pay GET on it. However, you are required to report the income on your HI state return. I would expect that since the address of the rental property that would be shown on your state return would be it's address outside of the state of HI, that this would not be a problem or raise any eyebrows in the HI dept of taxation.
