Yet Another Salesforce Tech Blog

In cases where Leads or Cases are updated via API you can control whether the assignment rules are run with the Sforce-Auto-Assign HTTP header

Salesforce runs the assignment rules when creating a case but also when updating case via the API (custom or standard). This is usually not wanted and the case can be re-assigned unexpectedly when updating a field on the case.

This can be prevented by setting the Sforce-Auto-Assign to FALSE in the HTTP header of the call that updates the case. Note that this also works if the case (or lead) is indirectly updated through a trigger if updating anohter object (for example CaseComment)

Read more here:

https://developer.salesforce.com/docs/atlas.en-us.api_rest.meta/api_rest/headers_autoassign.htm