Parking lot would be the US equivalent. While he was driving out of the car park (parking lot) ... or While he was driving away from the car park (parking lot) ... If it's a building in the US, it would likely be called a Parking Garage or Parking Structure. Perhaps Car Park is also used in the US but I think of it as BE.
San Luis Obispo Tribune on MSN: New SLO parking structure features variety of safety measures after deadly falls
New SLO parking structure features variety of safety measures after deadly falls
Orange County Register: Parking structure opens as first landside project in $600 million Dana Point Harbor renovation
Bryon Ward, a developer leading the landside renovation of Dana Point Harbor’s nearly $600 million remodel, enthusiastically walked across the top deck of the new three-level parking structure, ...
Parking structure opens as first landside project in $600 million Dana Point Harbor renovation
SanLuisObispo: SLO just rolled out its new gateless parking structure system. Here’s how to use it
The city of San Luis Obispo has installed a new gateless parking system at the Palm Street structure — confusing some downtown patrons . David Middlecamp dmiddlecamp@thetribunenews.com ...
SLO just rolled out its new gateless parking structure system. Here’s how to use it
archpaper: Parkitecture: Froedtert Hospital’s Blue Parking Structure exemplifies innovation, function, and elevated design
Parkitecture: Froedtert Hospital’s Blue Parking Structure exemplifies innovation, function, and elevated design
Vail Daily: Now 50, Vail parking structure is reaching the end of its useful life. Town staff says $12M in maintenance will stave off a 9-figure replacement project