Simultaneously transmitting (refracting) and reflecting reconfigurable intelligent surfaces (STAR-RISs) have been recently identified to improve the spectrum/energy efficiency and extend the communication range. However, their potential for enhanced concurrent indoor and outdoor localization has not yet been explored. In this paper, we study the fundamental limits, i.e., the Cramér Rao lower bounds (CRLBs) via Fisher information analyses, on the three-dimensional (3D) localization performance with a STAR-RIS at millimeter wave frequencies. The effect of the power splitting between refraction and reflection at the STAR-RIS as well as the power allocation between the two mobile stations (MSs) are investigated. By maximizing the principal angle between the two subspaces corresponding to the STAR-RIS reflection and refraction matrices, we are able to find the optimal solutions for these simultaneous operations. We verify that high-accuracy 3D localization can be achieved for both indoor and outdoor MSs when the system parameters are well optimized.