What makes you think it only leaks while parked. -
Oil
an oil leak
One way to find an oil leak on a 2000 Kia Sportage is to place a sheet of cardboard under the car when it is parked. By noting where the oil is dripping from, a person can determine about where the oil leak is on the motor. One place where oil may leak frequently is a full oil filter.
No there is currently no laws regulating a vehicle with an oil leak on a public roadway.
An oil leak.
HEadgasket failure, internal oil cooler leak.
The most common cause for occasional, small oil leaks is a worn seal or damaged gasket. The leaks are most visible when parked but occur constantly.
Does yours have air suspension on it. You may have a leak causing it to sit lower when you are not running. Ford Expeditions with air suspension is designed to lower when parked for easier access.
an oil pan leak is adding oil to the already polluted environment, causes you to drive with your car a bit low on oil at times, and causes unsightly stains under the car .aside from all this if you monitor the oil level and keep it where it should be , not much of anything else ,i can think of,
There should be no oil leaks on a new car, take it back to the dealer and let them look at it and repair your leak.
An old gasket that needs to be replaced.
This usually means a leak in the line somewhere, very small if it needs overnight for you to notice. But any fuel leak is dangerous, have it checked out.