It does seem quite strange. The punctuation on the second sentence is odd, too. I think it should be EITHER: "I don't know Tom; are you serious?" OR "I don't know, Tom. Are you serious?" The second alternative seems more natural to me, as whether one knows Tom or not would seem to have little relation to the subsequent question.

Once this problem is fixed, the exchange, as CK points out, would still be an odd one. Tom asks, say, Mary if she is serious. It doesn't seem natural, unless Mary is mentally ill, for her to then turn around and ask the identical question of Tom.

The simplest solution, in my opinion, would be to split up the group of two sentences into two separate Tatoeba entries.

It's based on something that I heard. "Are you serious about getting married?" "I don't know, Tom, are you serious?" It's possible that it doesn't make sense without context.

Ah, once the context is provided it does make a great deal more sense. Changing the sentence as Hybrid has done is very helpful to those who would not have known the original context. Now it is provided and will easily stand on its own. Good! :-)