Based on our personal experience, we've had to file separate state taxes while managing rental properties from out of state. I'm curious whether the same situation applies if we invest in REITs or similar fractional real estate investments. In 2017, we sold our 2-bedroom, 1-bathroom condo in Chicago after relocating to San Diego and had to file taxes in both Illinois and California.
Individual investors do not pay state income taxes for dividends from REITs outside the state of their residency. The REIT itself pays state income taxes for all the states it operates in.
If you hold ownership of a specific piece of property (fractional or otherwise) directly or through a disregarded entity (LLC taxed as partnership or sole proprietorship, for example), then yes, you'd be filing a state tax return for that state for the income derived from that property.