As a general rule, if the court has personal jurisdiction over the defendant driver in an automobile accident and the insurance company insured the defendant driver, personal jurisdiction over the insurance company is usually not a problem
The idea is that the insurance company is tied to the defendant. So if the defendant is subject to personal jurisdiction the court can assert personal jurisdiction over the defendant’s insurance company even if the insurance company does not have any business with the forum state.
More complicated questions arise where a plaintiff sues an insurance company for failing to provide coverage following an incident, such as a fire. In those cases, a court is not going to be able to assert personal jurisdiction simply because the insurance company is tied to a defendant. The court will likely follow a traditional analysis to determine whether there is personal jurisdiction: did the insurance company have sufficient contacts with the forum state and is the lawsuit related to those contacts?
¹ Actually she asked about venue but I think she meant personal jurisdiction. If I’m wrong, please let me know.