Out of state tax obligation

I live in Florida - a no income tax state. I have a rental in MD that I have to file a state tax form for at tax time. My question#1 is for those investing in a state that is a no income tax state (Florida, Texas,etc) but do not live in those states, what obligations are there, if any, to pay on the income earned from your rental properties to that state. My question#2 is opposite of #1. Living in Florida as I do, if I buy in Texas that does not have a state income tax, what obligations are there for reporting the income I would have earned on rental property in Texas. Thanks