You don't indicate how old the civil case is, but unless it is over 2 years old, you probably won't be able to get a discretionary dismissal, and unless it is more than 5 years old, you probably won't be able to get a mandatory dismissal.
Regardless, it is unlikely the civil court will advance the civil trial. It is often the case that the civil and criminal charges against the defendant stem from the same core set of facts. If the civil and criminal cases against such defendant are allowed to proceed abreast, that defendant will soon be faced with the untenable choice of defending himself in criminal court while facing a significant risk of losing substantial property or defending himself in civil court while facing a significant risk of losing substantial personal liberty. That forced dichotomy comports with neither governing case law nor governing statutes. (Cal. Evid. Code § 940; Code Civ. Proc.§ 2016(a).) Therefore, the remedy is often for the court in the civil case to issue a stay of the proceedings pending a final outcome in the criminal case.
Frank W. Chen has been licensed to practice law in California since 1988. The information presented here is general in nature and is not intended, nor should be construed, as legal advice for a particular case. This posting does not create any attorney-client relationship with the author. For specific advice about your particular situation, consult with your own attorney.
Although you don't describe the charges, generally I would say that the criminal case should be a defendant's focus of concern when compared to the potential repercussions of a civil claim. And, as they say on TV, anything you say in your civil case and and will be used against you in your criminal proceeding. So, it would be a fool's errand to provide the DA with a free set of sworn statements that could be used in your criminal case by putting the civil case out front.