If we had a rental house in another state but spent more on property tax, upgrades, etc., than we actually took in - do we need to file taxes with that state?

[PaulaM]

You don't mention the state but it is important to file even though you have losses. Those losses get carried forward to future years that you have a profit, or later when you decide to sell. 

[Hal_Al]

It depends on the state. Some have a gross income (rents received) filing requirement. 

[kng2]

Good call-out. The state is MI

[Hal_Al]

I'm not specifically familiar with MI. but a cursory reading of the following seems to say you don't need to file. 

https://www.michigan.gov/taxes/-/media/Project/Websites/taxes/Forms/2022/2022-IIT-Forms/Schedule-NR....