Can autistic people own a firearm?

When I was young (6) I was mistakenly diagnosed with autism. I am now very sure that I do not suffer from it. This was in the UK. Now I am 21 and live in Berkely, California, where I study. I know California has very bad gun laws but I still wish to purchase a handgun. I doubt whether they will let me if they think I am autistic. Is there any way to know if they know?