Process Integration/API PUT or POST to add Configuration Item?

The API documentation leads one to believe that it's possible to add configuration items by id to a ticket at creation or by updating, but I can't seem to make it work.

We're working on an inventory clean up and need to generate dozens of tickets over the course of several weeks to track the work. I need to be able to attach the related computers to the tickets. 

I definitely don't want to have to generate each ticket by hand, searching for and selecting each individual computer to relate it to the ticket, when I have CSV files I've generated with all the data required to plug into automated tickets.

I don't care if it's JSON or XML, I'd just like to not do this manually.