Both are right, depending on circumstances.
Generally - if project involves concentrating runoff anywhere it does not flow already, lies at any point below higher high water level (if tidal zone) or official floodplain limit if riparian (river), put water into a street or public drain that was not flowing there before, or diverts any mapped stream or drainage in any way, definitely yes. Between those, means yes for most any significant project and pretty much for anything that affect seasonally or perenially flowing water, as opposed to just rainfall runoff.
If just a within-yard french drain or swale but does not affect where it enter or leaves property, generally no.
Safest bet - have a plan drawn up (which should become part of the contract scope of work) and then take to pearmit department for their judgement. If your plan DOES require a SWQMP permit, requires detailed plans stamped by a civil engineer, so your best bet is to try to avoid that because between the design, plans, pearmits, etc it can drive the costa of your project up thousands of $ real quick.