Graphic Processing Units (GPUs) are commonly used to accelerate Convolutional Neural Networks (CNNs) for object detection and classification. As CNNs are employed in safety-critical applications, such as autonomous vehicles, their reliability must be carefully evaluated. In this work, we combine the accuracy of microarchitectural simulation with the speed of software fault injection to investigate the reliability of CNNs executed in GPUs. First, with a detailed microarchitectural fault injection on a GPU model (FlexGripPlus), we characterize the effects of faults in critical and user-hidden modules (such as the Warp Scheduler and the Pipeline Registers) in the computation of convolution over a suitably selected subset of tiles. Then, with software fault injection, we propagate the fault effects in the CNN. Thanks to our approach we are able, for the first time, to analyze the impact of faults affecting GPUs' hidden modules on a whole CNN execution (LeNET) without undermining the reliability evaluation correctness.