First not all soft-tops can have the top down, only those you see in you're garage or in the showroom with the top-down will do the trick. For example the Nissan 350Z convertable is shown with the roof down, but the RUF 3400s is not.
Next you need to do either a free run or a race with only one other car (such as the special conditions hall), and now you're top will be well and truely down.
This is however a topic that has been covered before and the search tool would have given you the answer.
To add on what Scaff said, you can also race top down in arcade mode. With convertables, the game will ask you if you want the top up or down. There ya go. 👍
To add on what Scaff said, you can also race top down in arcade mode. With convertables, the game will ask you if you want the top up or down. There ya go. 👍