FRB 180916.J0158+65 is one of the nearest, periodically repeating, and actively bursting fast radio bursts (FRBs) that has been localized to the outskirts of a spiral galaxy. In this work we study the FRB with the hard X-ray 14-195 keV data from the Burst Alert Telescope (BAT) on board The Neil Gehrels Swift Observatory. BAT uses coded mask technology giving a localization of ≲3' in the hard X-ray band, along with an accurate background estimation. BAT has been observing the source location in survey mode since 2020 February. The survey mode observations involve background subtracted spectra, integrated over a time span ranging 300-2000 s at the source location (from 2022 February-2022 January). We analyzed all the ~230 survey mode observations from BAT and checked for any signal in any of the observations. We did not detect any signal at >5σ confidence level in any of the observations. We could estimate a 5σ upper limit on the 14-195 keV flux, which ranged between 4.5 × 10-10-7.6 × 10-9 erg cm-2 s-1. At the source distance this relates to a 5σ upper limit on a luminosity of 5.08 × 1044-8.5 × 1045 erg s-1. With this estimate, we could rule out any persistent X-ray emission at the source location for these snapshots of BAT observations.