I got the data out of the BLS Consumer Expenditure Survey. They break down their numbers by income quintiles so thats a handy way to see some status broken down by income groups.
Here are the numbers in a table:
In general the lower income group folks are more likely to rent and the higher income people own more often. That follows from the simple fact that higher income makes it easier to buy and afford a home. Also, younger people are more likely to have lower income and less likely to have settled down and bought a home. So I figure some of this is correlated to age as well.
I find it interesting that lower income people are more likely to own a home without a mortgage than higher income people. 28% of the people in the bottom quintile own a home without a mortgage compared to only 18% of the people in the top quintile. I would hazard a guess that this is due to lower income people owning homes through inheritance or gift more than not. Homes can be passed down from generation to generation and if you're lower income you're more likely to keep an inherited home, whereas higher income folks are more likely to go out and buy a more expensive home. But again, this is just my theory.