In computer vision there has been significant research interest in assessing potential demographic bias in deep learning models. One of the main causes of such bias is imbalance in the training data. In medical imaging, where the potential impact of bias is arguably much greater, there has been less interest. In medical imaging pipelines, segmentation of structures of interest plays an important role in estimating clinical biomarkers that are subsequently used to inform patient management. Convolutional neural networks (CNNs) are starting to be used to automate this process. We present the first systematic study of the impact of training set imbalance on race and sex bias in CNN-based segmentation. We focus on segmentation of the structures of the heart from short axis cine cardiac magnetic resonance images, and train multiple CNN segmentation models with different levels of race/sex imbalance. We find no significant bias in the sex experiment but significant bias in two separate race experiments, highlighting the need to consider adequate representation of different demographic groups in health datasets.