I'm not sure what the rule is. Try driving through Oklahoma. Interstate Highway 44 becomes a toll highway. There are two lane roads that you can bypass some, but the main interstate highway is toll.
Just to the south side of Chicago, the main freeway becomes a tollway. Interstate 94/294/80?
Oregon/Washington is planning on replacing the main Interstate 5 Columbia river crossing. About half the money is supposed to be federal grant money, and half is supposed to be state funded between the two states. And there is a proposal to do the state proportion with tolls. I'm not excited about that, but I don't get up there very often. It will be interesting the impact if the I-5 crossing becomes a toll bridge, and the I-205 crossing remains free.
California puts tolls on many of the roads leading to San Francisco, or the bridges in and out of parts of the metro area. This includes the Golden Gate Bridge. I'm pretty sure they are state owned.