Within Teamwork Desk there is a REST API available for connecting your own applications.
To authenticate first generate an API key at
https://[your_installation]/desk/#myprofile/apikeys, then simply pass this API key as the password for HTTP Basic authentication as the username. The password field is ignored, and can be left empty or set to any text.
Note: Don't forget to prefix the URLs with
/desk; so it should be
/desk/v1/tickets/search.json, and not
/v1/tickets/search.json (that makes a call to the Teamwork Projects API).
For more information, see: Teamwork Desk API reference documentation