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Audio signals generated by the human body (e.g., sighs, breathing, heart, digestion, vibration sounds) have routinely been used by clinicians as indicators to diagnose disease or assess disease progression. Until recently, such signals were usually collected through manual auscultation at scheduled visits. Research has now started to use digital technology to gather bodily sounds (e.g., from digital stethoscopes) for cardiovascular or respiratory examination, which could then be used for automatic analysis. Some initial work shows promise in detecting diagnostic signals of COVID-19 from voice and coughs. In this paper we describe our data analysis over a large-scale crowdsourced dataset of respiratory sounds collected to aid diagnosis of COVID-19. We use coughs and breathing to understand how discernible COVID-19 sounds are from those in asthma or healthy controls. Our results show that even a simple binary machine learning classifier is able to classify correctly healthy and COVID-19 sounds. We also show how we distinguish a user who tested positive for COVID-19 and has a cough from a healthy user with a cough, and users who tested positive for COVID-19 and have a cough from users with asthma and a cough. Our models achieve an AUC of above 80% across all tasks. These results are preliminary and only scratch the surface of the potential of this type of data and audio-based machine learning. This work opens the door to further investigation of how automatically analysed respiratory patterns could be used as pre-screening signals to aid COVID-19 diagnosis.