I must confess I'm relatively unfamiliar with the concept of carnivalism in Mikhail Bakhtin, but I do know The Scarlet Letter and I'll share what I know in hopes of getting you started, anyway. I'm referencing an eNotes site on Bahktin, which I've cited below and which includes an rather extensive bibliography as well as a list of other kinds of references on him and his philosophies.
According to Bakhtin, carnival is the context in which distinct individual voices are heard, flourish and interact together....
[E]ach individual character is strongly defined, and at the same time the reader witnesses the critical influence of each character upon the other. That is to say, the voices of others are heard by each individual, and each inescapably shapes the character of the other.
The question, then, is whether this idea is applicable to The Scarlet Letter. By this definition, the idea of carnivalism can be found in this novel. A study could be made which intricately connects the major characters to each other as they continue to maintain their individuality.
One area to explore is the physicality of the three main characters--four if we count Pearl. It is the same sin which connects them all--adultery. The impact of that sin on each individual shows itself physically and goes on to impact those around them.
For example, Roger Chillingworth's wife has cuckolded him, and this begins his descent into an almost demonic seeker of revenge. We see it in his countenance as well as his entire body; and when his revenge is thwarted, he no longer has a reason to live. Hester has committed adultery, and she has also "dried up" as a woman. When she is reunited with her lover, she blossoms once again. While Hester wears an outward token of shame, Dimmesdale has internalized his guilt and it has manifested itself in his body. He is frail and weak and pale, a young man forced even to walk with the aid of a stick because he has so little strength. Pearl is an unruly and unusual child, acting in abnormally capricious and hurtful ways around the only other figures in her life--Hester, Arthur, and Roger. Her spell is broken when she receives her father's recognition and offers him the forgiveness he desires.
In each case, their physical changes or conditions reflect their inner turmoils and all of them contribute to the others' physical and emotional conditions.
This is an interesting idea to research and write about, and I'm confident you'll see even more connections as you further delve into the novel. Hawthorne's work is the perfect choice in which to explore Bakhtin's idea of carnivalism. Hope this helped. Best of luck!