Government agencies around the world use data-driven algorithms to allocate enforcement resources. Even when such algorithms are formally neutral with respect to protected characteristics like race, there is widespread concern that they can disproportionately burden vulnerable groups. We study differences in Internal Revenue Service (IRS) audit rates between Black and non-Black taxpayers. Because neither we nor the IRS observe taxpayer race, we employ a novel partial identification strategy to estimate these differences. Despite race-blind audit selection, we find that Black taxpayers are audited at 2.9 to 4.7 times the rate of non-Black taxpayers. The main source of the disparity is differing audit rates by race among taxpayers claiming the Earned Income Tax Credit (EITC). Using counterfactual audit selection models, we find that maximizing the detection of underreported taxes would not lead to Black taxpayers being audited at higher rates. In contrast, certain policies tend to increase the audit rate of Black taxpayers: (1) designing audit selection algorithms to minimize the "no-change rate"; (2) targeting erroneously claimed refundable credits rather than total under-reporting; and (3) limiting the share of more complex EITC returns that can be selected for audit. Our results highlight how seemingly technocratic choices about algorithmic design can embed important policy values and trade-offs.