While CRISPR-Cas13 systems excel in accurately targeting RNA, the potential for collateral RNA degradation poses a concern for therapeutic applications and limits broader adoption for transcriptome perturbations. We evaluate the extent to which collateral RNA cleavage occurs when Rfx Cas13d is delivered via plasmid transfection or lentiviral transduction and find that collateral activity only occurs with high levels of Rfx Cas13d expression. Using transcriptome-scale and combinatorial CRISPR pooled screens in cell lines with low-copy Rfx Cas13d, we find high on-target knockdown, without extensive collateral activity regardless of the expression level of the target gene. In contrast, transfection of Rfx Cas13d, which yields higher nuclease expression, results in collateral RNA degradation. Further, our analysis of a high-fidelity Cas13 variant uncovers a marked decrease in on-target efficiency, suggesting that its reduced collateral activity may be due to an overall diminished nuclease capability.