Many kinds of criminal acts can be the basis of civil lawsuits for damages (money). For example, someone who commits an assault and battery might be the defendant in both a criminal prosecution brought by the government and a civil case brought by the victim. (Dual cases in this situation don’t invoke double jeopardy because only one is criminal.)
When criminal and civil charges are simultaneously pending, litigation can get thorny. For example, the civil plaintiff might want to take the deposition of the defendant. But because the criminal case is unresolved, the defendant’s lawyer will likely advise him to remain silent in order to avoid self-incrimination.
When civil and criminal cases share the same underlying facts, judges typically have discretion in deciding whether to grant a stay or continuance in the civil matter. (The criminal case almost always takes priority.) (State ex rel. Stovall v. Meneley, 271 Kan. 355 (2001).) Judges frequently opt for the stay or continuance because waiting for resolution of the criminal case can simplify the proceedings. Not only can issues like refusal to testify be avoided, but the criminal litigation can resolve some of the issues involved in the civil suit.
Example: A former employee faces criminal charges and a civil lawsuit by her former employer for stealing company funds. The employee defendant moves for a stay of the civil case until resolution of the criminal case. The civil court judge decides to stay the civil case until the employee is either convicted or acquitted—not only will the stay alleviate the self-incrimination problem, but conviction in the criminal case will prevent her from denying the essential factual allegations in the civil case. (See Peterson v. Therma Builders, Inc., 958 So. 2d 977 (Fla. Dist. Ct. App. 2007).)
If you are the subject of both criminal and civil proceedings, make sure to consult with one lawyer or more—perhaps one for the criminal case and one for the civil matter. A knowledgeable attorney will be able to advise you of the applicable law and propose a strategy for dealing with both cases.