If you are a standard or administrative user, you can conduct a basic conflicts check using Casefleet.

First, visit the global contacts menu via the vertical menu on the left. Next, search for the appropriate contact and click the name to open the Contact's detail page. From here, click the "Cases" link on the left.

You will see a list of all cases to which the contact has been assigned. As you can see in the example below, the contact Sally Jones is involved in three cases.