According to someone who was there. A blog post at GoodyBlog:

At the Carnegie Hall reading event, a teenager stood up and spoke from the bottom of her heart about how the Harry Potter books had given her the strength to be herself. She then asked: “Did Dumbledore ever find love?”

JKR was clearly moved and replied, "I owe you a truthful answer after how much you opened yourself up to me. I always thought of Dumbledore as gay.”

The entire crowd burst into spontaneous, prolonged cheers and applause. I did too! It wasn’t because of the answer (who cares really)— I think it was because it's so rare to witness a completely honest exchange in a setting as public and orchestrated as a Carnegie Hall event. It was clear that JKR didn't plan to out Dumbledore. She just cares about being true to her readers.

She’s wasn’t there to sell more books or to promote her next project, she was just there to connect, honor, and try to give back the love that her fans give her.

JKR said that the Harry Potter Series was a prolonged argument for tolerance, and a plea for an end to bigotry. Her parting words: “I think that’s one of the reasons that some people don't like the books, but I think that it's a very healthy message to pass on to younger people—that you should question authority.”