In the bath tub is my guess.
But it doesn't look like you have to be wearing one. And depending on where you are paddle boarding the rules may not even apply.
"WASHINGTON - The U.S. Coast Guard in a decisional memo dated Oct.3, classified paddleboards as vessels in accordance with Title 1 United States Code, Section 3.
This classification means that when used beyond the narrow limits of a swimming, surfing, or bathing area, no person may use a paddleboard unless in compliance with the Navigation Rules, and applicable carriage requirements for this type of vessel.
This may include a Coast Guard approved life jacket for each person on board, a sound producing device, visual distress signals, and proper navigation lights. A police-type whistle and a flashlight comply with these requirements."
At least they say "may include" not must.