FRB 180916.J0158+65 is one of the nearest, periodically repeating, and actively bursting fast radio burst (FRB) which 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 $\lesssim 3$ arc-minute in the hard X-ray band, along with an accurate background estimation. BAT has been observing the source location in survey mode since February 2020. The survey mode observations involves background subtracted spectra, integrated over a time span ranging $300-2000$ seconds, at the source location (from Feb 2020-Jan 2022). We analyzed all the $\sim 230$ survey mode observations from BAT and checked for any signal in any of the observations. We did not detect any signal at $>5\sigma$ confidence level in any of the observations. We could estimate a $5\sigma$ upper limit on the $14-195$ keV flux, which ranged between $4.5\times 10^{-10} - 7.6\times 10^{-9}\, \rm erg\, cm^{-2}\, s^{-1}$. At the source distance this relates to a $5\sigma$ upper limit on luminosity of $5.08\times 10^{44}- 8.5\times 10^{45} \rm erg\, s^{-1}$. With this estimate, we could rule out any persistent X-ray emission, at the source location for these snapshots of BAT observations....