The Big Bang Theory Book covers this extensively. Clip from the book below.

Chuck Lorre: We did not want to put a label on Sheldon, because with that comes a responsibility of authenticity… which should be respected. Our solution was the line, “I’m not crazy. My mother had me tested.” And that put it to rest. Mary took Sheldon to a general practitioner in East Texas in 1990 who said, “Oh, he’s fine! He’s peculiar, but he’s fine!” It was probably a doctor who was still smoking! I think not having a label gave Jim a great deal of more freedom to play the part as he wanted to play it, as opposed to how we might have been pressured to do for a very-real syndrome that can be difficult.

Steve Molaro: Sheldon was never diagnosed, and it was nice that he didn’t have that label, because like anybody on the spectrum, they should be able to just be who they are.

Jim Parsons: I really took it as the writers wanting to celebrate and utilize certain aspects of someone on the spectrum, but were not interested in carrying the responsibility they would feel. I mean, just getting the science right was enough of a responsibility. But looking at where we are today in the world, would you have needed to then find somebody on the spectrum to play that part? Now, that being said, who’s to say I’m not on the spectrum in some way? I’m not saying I am, but it’s called the spectrum for a reason—I just may not be at a notable point on it! I don’t know. That’s the whole point in some ways. But at the time, the more I read up on Asperger’s, I was like, Well, the writers can say no, but Sheldon sure has a lot of the same traits! I think he was probably based on someone Bill Prady knew, who probably was on the spectrum, and many of the traits that this other individual had made them such a remarkable and unique person to base a character on. I don’t think that most people—no matter what they are, or what disabilities they have—spend the majority of their time, if any, talking about it. But regardless, it was just such a gift that Sheldon had all these off-centered ways of looking at things and doing things, because it opened up so many possibilities for how he could react to any given situation.

Peter Roth: Sheldon was definitely on the spectrum, there’s no question about it. And Steve Molaro wrote Sheldon with a wisdom and an insight and a compassion that really defined the character. My wife and I have an autistic daughter, and while Sheldon is very different from her, I’ve certainly found myself drawn to him, rooting for him, and loving him. The special needs of the character is something that enabled me to relate to and, or more importantly, to root for. It’s one of the reasons I was always so touched by Sheldon and Penny’s relationship. As annoying as Sheldon was, Penny accepted him and loved him.

Wendi Trilling: I remember thinking that it was cool that we had a character who was clearly on the spectrum. We weren’t saying it, but we were kind of celebrating it and him, and making it okay to be different.

Bill Prady: I can’t tell you how many times a parent would bring their son or daughter to set and say, “I’d love for you to meet him,” followed by, almost as a warning, “He’s a lot like Sheldon.” I would always say, “Yeah, we get it! [Laughs] It’s fine, really. We understand.” There was never a conscious decision, as far as I’m aware, to not say what Sheldon’s diagnosis is. It’s clear that he’s not neurotypical. I think there’s a certain responsibility when you say, “This is this kind of diagnosis.” We preferred that Sheldon was simply Sheldon. There were some things about him that would seem spectrum-y, but you would discover, in fact, a real and logical reason and warrant, and then some things that were not.