Wearable devices are rapidly improving our ability to observe health-related processes for extended durations in an unintrusive manner. As part of the Lived Experiences Measured Using Rings Study (LEMURS), we collected heart rate measurements using the Oura ring (Gen3) for over 25,000 sleep periods and self-reported mental health indicators from roughly 600 first-year university students in the United States during the fall semester of 2022. Using clustering techniques, we find that the sleeping heart rate curves can be broadly separated into two categories that are mainly differentiated by how far along the sleep period the lowest heart rate is reached. Sleep periods characterized by a longer time to reach the lowest heart rate are also associated with shorter deep and REM sleep and longer light sleep, but not a difference in total sleep duration. Aggregating sleep periods at the individual level, we find that consistently reaching the lowest heart rate later during sleep is a significant predictor of (1) self-reported impairment due to anxiety or depression, (2) a prior mental health diagnosis, and (3) firsthand experience in traumatic events. This association is morwe pronounced among females. Our results show that the shape of the sleeping heart rate curve, which is only weakly correlated with descriptive statistics such as the average or the minimum heart rate, is a viable but mostly overlooked metric that can help quantify the relationship between sleep and mental health.