Yes, under certain circumstances.
If you are a non-resident and Utah can still exercise jurisdiction over your case, this is referred to as “long-arm jurisdiction”. The statute which submits non-resident parties to Utah’s jurisdiction is found in Utah Code §78B-3-205.
The term “jurisdiction” refers to a court’s power to hear and decide a person’s case. In some situations, a court in a state where you do not currently reside may still have jurisdiction over you, depending upon the kind of case. Divorce is one of those kinds of cases.
Could Utah have jurisdiction over you in a divorce case filed in Utah, even if you don’t live there now?
In the context of a divorce (or another family matter involving paternity, child support, or separate maintenance), Utah may have jurisdiction over your case in two situations:
First, if you resided in the state of Utah during your marital relationship.
Second, if the act giving rise to the claim occurred in Utah (so long as that act is not a mere omission, failure to act, or occurrence over which the defendant had no control).
Utah Family Law, LC | divorceutah.com | 801-466-9277
 78B-3-205. Acts submitting person to jurisdiction.
Any person (whether or not a citizen or resident of this state) who does any of the following acts is subject to the jurisdiction of the courts of this state. With respect to actions of divorce, separate maintenance, or child support:
(6) having resided in the marital relationship, within this state notwithstanding subsequent departure from the state; or the commission of the act giving rise to the claim in this state (so long as that act is not a mere omission, failure to act, or occurrence over which the defendant had no control);
(7) the commission of sexual intercourse within this state which gives rise to a paternity suit under Title 78B, Chapter 15 of the Utah Uniform Parentage Act, to determine paternity for the purpose of establishing responsibility for child support.