In general its a bad idea to take a convertible through a car wash.
The top is canvas, so you should treat it like any other canvas top. Don't use soaps on the top unless they were specifically made for a canvas top. I just remove dirt with a brush and a specific canvas cleaner, you don't want to use just any soap because the canvas will absorb its oils and become dirty very quickly from that point forward. You also want to keep the top colorfast and looking good, but at the same time waterproof. Without putting a treatment on the top, it isn't waterproof and will develop issues as it ages. I use a product called 303, but there's also Ragg Top, they keep the top in nice shape, waterproof and help prevent fading. It takes about an hour to apply because you have to mask off the car (this stuff is great, but you don't want it on your paint), but it only needs to be done about twice a year. Its a little extra work, but it will keep the top looking good and water proof.