First find the form which contains the filed that the restriction should be placed on.
Out of the box forms for Service Desk can be found in the following directory:
Then search for the filed to be updated, for example if the field header is "New Assignee" an entry similar to the text below should be located:
PDM_MACRO name=dtlLookup hdr="New Assignee"
To only allow a specific type of contact to be entered on this form, such as Analysts, add the following to this line:
Where "2307" is the Analyst contact type id.