Zoho Desk API - Add inbound to thread

Zoho Desk API - Add inbound to thread

I am trying to integrate with the new OAuth Zoho Desk API, and having a problem.

I would like to add to the "Thread" of an open ticket, for an inbound message, but don't see an option for this in the thread api.

Use case:
 - Inbound message comes in (via Twilio SMS with custom webhook on our server)
 - Agent replies back by adding a comment to the ticket (Zoho webhook posts back to our server, and we send the message to Twilio to send SMS)
 - End user sends another reply <---- Problem. How do I add this to the thread of the current ticket? If I add it as a comment, it assigns an agent automatically. I want it to assign a contact to that comment.