Precise identification of mouse brain microscopy images is a crucial first step when anatomical structures in the mouse brain are to be registered to a reference atlas. Practitioners usually rely on manual comparison of images or tools that assume the presence of complete images. This work explores Siamese Networks as the method for finding corresponding 2D reference atlas plates for given partial 2D mouse brain images. Siamese networks are a class of convolutional neural networks (CNNs) that use weight-shared paths to obtain low dimensional embeddings of pairs of input images. The correspondence between the partial mouse brain image and reference atlas plate is determined based on the distance between low dimensional embeddings of brain slices and atlas plates that are obtained from Siamese networks using contrastive learning. Experiments showed that Siamese CNNs can precisely identify brain slices using the Allen mouse brain atlas when training and testing images come from the same source. They achieved TOP-1 and TOP-5 accuracy of 25% and 100%, respectively, taking only 7.2 seconds to identify 29 images.