The short answer is Yes. Since the trust generates income from the state where the property is located, the beneficiary who receives a proportionate share of the trust income has income sourced from that state and therefore is required to file an income tax return with that state.
Having said that, the amount of tax the beneficiary pays to the state where the property is located may be able to offset a substantial amount if not the entire amount of state tax paid from the tax s/he pays to the resident tax return as the income from the 1041 K-1 is also taxed by the resident state. This way, there is no double taxation. This is assuming the resident state has a state tax. But if the resident state has no income tax, then the income is only taxed once anyway.
