The positron emission tomography (PET) insert for a magnetic resonance imaging (MRI) system that implements the radiofrequency (RF) built-in body coil of the MRI system as a transmitter is designed to be RF-transparent, as the coil resides outside the RF-shielded PET ring. This approach reduces the design complexities (e.g., large PET ring diameter) related to implementing a transmit coil inside the PET ring. However, achieving the required field transmission into the imaging region of interest (ROI) becomes challenging because of the RF shield of the PET insert. In this study, a modularly RF-shielded PET insert is used to investigate the RF transparency considering two electrical configurations of the RF shield, namely the electrical floating and ground configurations. The purpose is to find the differences, advantages and disadvantages of these two configurations. Eight copper-shielded PET detector modules (intermodular gap: 3mm) were oriented cylindrically with an inner diameter of 234mm. Each PET module included four-layer Lutetium-yttrium oxyorthosilicate scintillation crystal blocks and front-end readout electronics. RF-shielded twisted-pair cables were used to connect the front-end electronics with the power sources and PET data acquisition systems located outside the MRI room. In the ground configuration, both the detector and cable shields were connected to the RF ground of the MRI system. In the floating configuration, only the RF shields of the PET modules were isolated from the RF ground. Experiments were conducted using two cylindrical homogeneous phantoms in a 3T clinical MRI system, in which the built-in body RF coil (a cylindrical volume coil of diameter 700mm and length 540mm) was implemented as a transceiver. For both PET configurations, the RF and MR imaging performances were lower than those for the MRI-only case, and the MRI system provided specific absorption ratio (SAR) values that were almost double. The RF homogeneity and field strength, and the signal-to-noise ratio (SNR) of the MR images were mostly higher for the floating PET configuration than they were for the ground PET configuration. However, for a shorter axial field-of-view (FOV) of 125mm, both configurations offered almost the same performance with high RF homogeneities (e.g., 76±10%). Moreover, for both PET configurations, 56±6% larger RF pulse amplitudes were required for MR imaging purposes. The increased power is mostly absorbed in the conductive shields in the form of shielding RF eddy currents; as a result, the SAR values only in the phantoms were estimated to be close to the MRI-only values. The floating PET configuration showed higher RF transparency under all experimental setups. For a relatively short axial FOV of 125mm, the ground configuration also performed well which indicated that an RF-penetrable PET insert with the conventional design (e.g., the ground configuration) might also become possible. However, some design modifications (e.g., a wider intermodular gap and using the RF receiver coil inside the PET insert) should improve the RF performance to the level of the MRI-only case.