It's the same as a normal relationship. Yes, you can date a person with down syndrome. The main reason people don't is because they are too slow. People with down syndrome don't fully understand things, and in turn, tend to be unable of efficient communication. They might not know what to do in a relationship. What is appropriate and what is not. They are, essentially, like children; not the brightest, but honest and innocent(in most cases. Depending on who they hang out with, they can become mean and unhappy people). However, if you genuinely like the person, then I don't see why you can't date them. Just don't take advantage of them, and be patient.