Surveying cryptic, sparsely distributed taxa using autonomous recording units, although cost-effective, provides imperfect knowledge about species presence. Summertime bat acoustic surveys in North America exemplify the challenges with characterizing sources of uncertainty: observation error, inability to census populations, and natural stochastic variation. Statistical uncertainty, if not considered thoroughly, hampers determining rare species presence accurately and/or estimating rangewide status and trends with suitable precision. Bat acoustic data are processed using an automated workflow in which proprietary or open-source algorithms assign a species label to each recorded high-frequency echolocation sequence. A false-negative occurs, if a species is actually present but not recorded and/or all recordings from the species are of such poor quality that a correct species identity cannot be assigned to any observation. False positives for a focal species are a direct result of the presence and incorrect identification of a recording from another species. We compare four analytical approaches in terms of parameter estimation and their resulting (in)correct decisions regarding species presence or absence using realistic data-generating scenarios for bat acoustic data within a simulation study. The current standard for deciding species presence or absence uses a multinomial likelihood-ratio test p value (maximum likelihood estimate [MLE]-metric) that accounts for known species misidentifications, but not imperfect detection and only returns a binary outcome (evidence of presence or not). We found that the MLE-metric had estimated median correct decisions less than 60% for presence and greater than 85% for absence. Alternatively, a multispecies count detection model was equivalent to or better than the MLE-metric for correct claims of rare species presence or absence using the posterior probability a species was present at a site and, importantly, provided unbiased estimates of relative activity and probability of occurrence, creating opportunities for reducing posterior uncertainty through the inclusion of meaningful covariates. Single-species occupancy models with and without false-positive detections removed were insufficient for determining local presence because of substantially biased occurrence and detection probabilities. We propose solutions to potential barriers for integrating local, short-term and rangewide, long-term acoustic surveys within a cohesive statistical framework that facilitates determining local species presence with uncertainty concurrent with estimating species–environment relationships.