Issues with inflated false positive rates (FPRs) in brain imaging have recently received significant attention. However, to what extent FPRs present a problem for voxelwise analyses of Positron Emission Tomography (PET) data remains unknown. In this work, we evaluate the FPR using real PET data under group assignments that should yield no significant results after correcting for multiple comparisons. We used data from 159 healthy participants, imaged with the serotonin transporter ([11C]DASB; N = 100) or the 5-HT4 receptor ([11C]SB207145; N = 59). Using this null data, we estimated the FPR by performing 1,000 group analyses with randomly assigned groups of either 10 or 20, for each tracer, and corrected for multiple comparisons using parametric Monte Carlo simulations (MCZ) or non-parametric permutation testing. Our analyses show that for group sizes of 10 or 20, the FPR for both tracers was 5-99% using MCZ, much higher than the expected 5%. This was caused by a heavier-than-Gaussian spatial autocorrelation, violating the parametric assumptions. Permutation correctly controlled the FPR in all cases. In conclusion, either a conservative cluster forming threshold and high smoothing levels, or a non-parametric correction for multiple comparisons should be performed in voxelwise analyses of brain PET data.