Correlation-based functional MRI connectivity methods typically impose a temporal sample independence assumption on the data. However, the conventional use of temporal filtering to address the high noise content of fMRI data may introduce sample dependence. Violation of the independence assumption has ramifications for the distribution of sample correlation which, if unaccounted for, may invalidate connectivity results. To enable the use of temporal filtering for noise suppression while maintaining the integrity of connectivity results, we derive the distribution of sample correlation between filtered timeseries as a function of the filter frequency response. Corrected distributions are also derived for statistical inference tests of sample correlation between filtered timeseries, including Fisher's z-transformation and the Student's t-test. Crucially, the proposed corrections are valid for any unknown true correlation and arbitrary filter specifications. Empirical simulations demonstrate the potential for temporal filtering to artificially induce connectivity by introducing sample dependence, and verify the utility of the proposed corrections in mitigating this effect. The importance of our corrections is exemplified in a resting state fMRI connectivity analysis: seed-voxel correlation maps generated from filtered data using uncorrected test variates yield an unfeasible number of connections to the left primary motor cortex, suggesting artificially induced connectivity, while maps acquired from filtered data using corrected test variates exhibit bilateral connectivity in the primary motor cortex, in conformance with expected results as seen in the literature.