Allow API to set "inbox" status

I'm using the .net api a couple different places, and I would like to be able to set the ticket "inbox" status so that I can specify it the ticket should show in the inbox or not. Is there any possibility of this field being accessible via the API?

Thanks!

Tickets enter the Inbox automatically when their being updated by external source and when the customer replies. There isn't currently a way to control this or remove tickets from it automatically. Thanks for asking.