What are the relevant US regulations on doing something like this? I know some streams are crucial ecologically. But is it mostly regulated on a national, state or local level?
Playing with any water system requires permission from the water management district in your local area, or the health department, or both. Plans would need to be drawn and stamped by a civil engineer, inspected and approved and then final inspected after construction in order to be put to use.
As other commenters have mentioned, it's a state-level thing, but in reality most (all?) states handle permitting and enforcement at the city and county level. In many rural counties you could get away with this without a problem. Is it technically against the law? Sure. But county officials may not notice, care, or have the resources to enforce the rules depending on where you are. Many rural areas operate under a live-and-let-live approach when it comes to individual property, as long as you don't cross anyone with political pull or make a gigantic obvious mess.
I believe it's mostly state level, and at least in my state this would indeed be illegal without a permit, which I'm quite sure would not be granted in this case.
