There are still debates whether particle acceleration in solar flares may occur due to interruption of electric currents flowing along magnetic loops. To contribute to this problem, we performed the first statistical study of relationships between flare hard X-ray (HXR; $50-100$ keV) sources observed by the textit{Ramaty High-Energy Solar Spectroscopic Imager} (RHESSI) and photospheric vertical electric currents (PVECs, $j_{r}$) calculated using vector magnetograms obtained with the Helioseismic and Magnetic Imager (HMI) on-board the textit{Solar Dynamics Observatory} (SDO). A sample of 48 flares, from C3.0 to X3.1 class, observed in central part of the solar disk by both instruments in 2010--2015 was analyzed. We found that $approx 70$% of all HXR sources overlapped with islands or ribbons of enhanced ($left| j_{r} right| gtrsim 10^{4}$ statampere~cm$^{-2}$) PVECs. However, less than $approx 40$% of the HXR sources overlapped with PVEC maxima, with an accuracy of $pm 3^{primeprime}$. More than in half of the flares there were HXR sources outside regions of enhanced PVECs. We found no correlation between intensity of the HXR sources and PVEC density or total PVEC under them. No systematic dissipation of PVECs under the HXR sources was found during the flares. Collectively, the results do not support the current-interruption flare models. However, the results indicate the importance of the presence of longitudinal currents in flare regions. Understanding of their specific role in the processes of energy release, plasma heating, and acceleration of particles requires further investigation.
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