The OS X Contacts.app sadly has a bug, which causes it to freeze from time to time when editing a contact in a CardDAV account. This bug already affected previous OS X versions, but got even worse in OS X 10.11 (El Capitan). We believe that this bug is related to the sandboxing security mechanisms of OS X.

We've reported the problem as rdar://problem/23311441 via the Apple Bug Reporter and hope that they'll fix it in a future system update.

Update (2016-05-16)
Apple released OS X 10.11.5 on May 16th in 2016. With this update we are no longer able to reproduce this issue. It's still a little early to say, but it looks like Apple fixed the issue. Let us know if you are still experiencing the problem after installing the system update.