Oh no, we’re sorry to hear your car is leaking! It’s good that you noticed it though. Many drivers don’t look under their car to see if anything is leaking until the leak gets so bad it can’t be missed, and by then you might have bigger problems on your hands.
Yes, your water pump can leak even if your engine is off. Parts can develop tiny cracks or holes. Hoses can be damaged, which can cause them to rupture. It’s possible, but you shouldn’t start worrying about replacing any parts yet.
First, let’s identify what fluid is leaking from your car. If you can, try to identify the area where the liquid leaks from and put a few paper towels under that area. What color is the liquid that’s leaking?
Dark brown or blackish is usually motor oil
Light brown might be motor oil or dirty transmission fluid. If it smells really bad, it could be gear lubricant
Orange liquid is either antifreeze, transmission fluid, or air conditioning condensation
Red or pink liquid is power steering fluid or transmission fluid
Green or yellow liquid is usually antifreeze or coolant
Blue liquid is usually windshield wiper fluid. Some Hondas use blue coolant, too
Clear liquid is probably air conditioning condensation. It might be brake fluid, but if your brakes feel fine, it’s the car’s AC
If it’s air conditioning condensation, it’s nothing to worry about. But if there’s some color to the liquid, take your car to a mechanic as soon as possible. This is especially true if you hear odd sounds when driving or notice anything different about the car’s general handling or performance.