If a personal injury case was dismissed without prejudice how long after does the plaintiff have to refile the case?

The plaintiff can refile any time within the original statute of limitations. The statute of limitations is the time period to bring a lawsuit. For a personal injury case, it is measured from the time of the injury or accident. In Missouri (each state has its own statute of limitations), the limitations period for a personal injury matter appears to be 5 years. That means that, in the case of dismissal without prejudice, the would-be plaintiff may refile the action at any time up to 5 years from the date of the event or injury giving rise to his or her claim. All that matters is the statute of limitations; there are no additional time periods or restrictions measured from when the dismissal was granted.

Missouri has a statute which can extend the time to file for plaintiff under certain circumstances. Under Section 516.230 of the Missouri Revised Statutes, as long as the action was initially commenced within the statute of limitations period, the plaintiff has up to a year after a "nonsuit" to bring his or her suit again. A "nonsuit" is a special kind of dismissal without prejudice: it's when the plaintiff either voluntary withdraws (or does not prosecute) his suit  or does not appear for court. Not all dismissals without prejudice are nonsuits: for example, failure to establish jurisdiction by proper service on the defendant is not a nonsuit and would not extend the time to refile the matter.This is also not the same thing as adding an extra year to the statutory period, unless the nonsuit was right at the end of the statutory period. To take three examples, to illustrate this statute's operation:* Nonsuit more than one year before the statutory period runs out or expired: nothing is added.* Nonsuit with 9 months left in the statutory period; the plaintiff gets 1 year from the dismissal, which effectively adds 3 months to the statutory period.* Nonsuit at the very end of the statutory period: the extra year effectively adds a year to the statutory period.Note that in a very few cases, the statutory period can even be effectively extended for more than a year: if the original suit was brought near the end of the statutory period, then nonsuited, say, 3 months after the statute of limitations has expired, the plaintiff gets a year from the nonsuit, or up to one year and three months after the expiration of the statute of limitations, to bring an action.