Keep in mind most of those regulations are just building permits no restriction on the capacity captured or stored, and in a lot of them it is encouraged that you capture rainwater too. It eases the infrastructure load without tapping into aquafers that farmers use for irrigation during dry spells. Looks like on the west coast the only states that have regulations and don't encourage it are Oregon and Idaho while Nevada (basically a desert so it is kinda understandable the state wants to capture all the water it can get) is the only one that has very limited access to water capture.Not very well informed, but seems like the eastern US doesn’t have a lot of regulations for water use for a homeowner, but can be very restrictive in the western states.
Riparian rights is a term that comes to mind. Honestly don’t recall what it entails in detail.
I don't include the states like California, New Mexico, Arizona, or Texas because they are regulated but they offer incentives to do it so you get to save money in 2 ways rather than just the lower water consumption.
Other than that it appears that most other states either don't care either way or encourage it without requiring permits.