As a decision as whether or ot Tamcest exists is up to you.
In a deleted scene from "Our Misses Reyolds" River asks that Sheperd Book marry her and Simon. When Simon explains that they can't marry, River is still insistant o them "mating" or "doppling" as she spews adjectives for marriage. After a lengthy argument and a swift kick in the shin (by River of course) River stuffs a pillow up the front of her shirt and states that they must marry because she is "in the family way."
In an interview, and I paraphrase, Summer Glau stated that, in the future, she would "like to play another Whedon character that was not in love with her brother."
It is often rumoured, that Whedon stated in an interview that he had originally had a scene where River kissed Simon.
However, all of these can be made invalid if you account for River's mental instability, and that if she does like him, the end scene of Serenity between Simon and Kaylee proves that it was unrequited.