Around the world, policymakers and news reports have warned that domestic violence (DV) could increase as a result of the COVID-19 pandemic and the attendant restrictions on individual mobility and commercial activity. However, both anecdotal accounts and academic research have found inconsistent effects of the pandemic on DV across measures and cities. We use high-frequency, real-time data from Los Angeles on 911 calls, crime incidents, arrests, and calls to a DV hotline to study the effects of COVID-19 shutdowns on DV. We find conflicting effects within that single city and even across measures from the same source. We also find varying effects between the initial shutdown period and the one following the initial re-opening. DV calls to police and to the hotline increased during the initial shutdown, but DV crimes decreased, as did arrests for those crimes. The period following re-opening showed a continued decrease in DV crimes and arrests, as well as decreases in calls to the police and to the hotline. Our results highlight the heterogeneous effects of the pandemic across DV measures and caution against relying on a single data type or source.