A defendant can assert his 5th amendment rights in a civil case just as he can in a criminal case. He does not admit liability or negligence by doing so.
The difference between taking the 5th in a civil case and a criminal case is that the jury in a civil case may infer negligence from the defendant's silence. The jury in a criminal case may not consider the defendant's silence for any reason and may not infer guilt.
Since the Supremes are taking up the question means it is an issue, which means some jurisdictions allow it.