Measuring the prevalence of active SARS-CoV-2 infections in the general population is difficult because tests are conducted on a small and non-random segment of the population. However, people admitted to the hospital for non-COVID reasons are tested at very high rates, even though they do not appear to be at elevated risk of infection. This sub-population may provide valuable evidence on prevalence in the general population. We estimate upper and lower bounds on the prevalence of the virus in the general population and the population of non-COVID hospital patients under weak assumptions on who gets tested, using Indiana data on hospital inpatient records linked to SARS-CoV-2 virological tests. The non-COVID hospital population is tested fifty times as often as the general population, yielding much tighter bounds on prevalence. We provide and test conditions under which this non-COVID hospitalization bound is valid for the general population. The combination of clinical testing data and hospital records may contain much more information about the state of the epidemic than has been previously appreciated. The bounds we calculate for Indiana could be constructed at relatively low cost in many other states.