Isogeometric analysis (IGA) has recently gained popularity for the simulation of electromagnetic problems. It is especially well-suited for the simulation of electric motors, as these machines have a cylindrical geometry which cannot be represented well by classical finite elements. In the simulation of electric machines, refinement is often necessary in certain parts of the machine to obtain accurate solutions. As classical IGA requires a conforming control mesh also across patch-borders and due to the tensor product construction of the B-spline basis functions, local refinement poses one of the main challenges in the simulation of real-world problems. Several approaches for local refinement are being researched, including T-splines and hierarchical B-splines. In magnetostatic and magnetoquasistatic settings using a magnetic vector potential approach requires a gauging technique to obtain a unique solution. One method that has proven to be suitable for the isogeometric case is the tree-cotree decomposition which can be employed to remove the discrete kernel of the system. In this work, we explore how a tree-cotree decomposition can be applied to locally refined B-spline spaces using hierarchical B-splines. This work is supported by the joint DFG/FWF Collaborative Research Centre CREATOR (CRC – TRR361/F90) at TU Darmstadt, TU Graz and JKU Linz and the Graduate School CE within the Centre for Computational Engineering at Technische Universität Darmstadt.