It is halachicly assur for either spouse to litigate in secular court (arkaos) to adjudicate who gets what money, assets, support or custody. (They can submit the beis din decision to the court as their agreed upon settlement. If one party acts in contempt of beis din then b”d can make an exception and permit the other party to use of arkaos.) If she opens a case in secular court and receives money or assets from him through such a verdict, he has the halachic right (I can supply teshuvos from Rav Elyashev, Rav Shternbuch, Rav M. Klein, etc. to this effect) to withhold the Get until she reverses that and returns to him her ill gotten gains awarded to her by a civil court. Rav Shternbuch’s teshuva in such a case rules that he can even get a heter meah to remarry while the Get is held by b”d until she returns those assets to him.
The halacha is that a Get is given after all outstanding divorce/gittin issues has been finalized and settled by beis din. A civil divorce has no bearing on Hilchos Gittin as to whether a Get is obligatory.