Slovak troops fought as part of the Axis coalition in the Soviet Union, mostly in the Ukraine. The killing of Jews was not hidden, so it would be highly likely that some Slovakians witnessed the shootings, and, perhaps, some participated. Einsatsgruppe D, under SS-Gruppenführer Otto Ohlendorf, was the main killing unit in Ukraine.
Reference: Rap nr 812 (AES 3368/42 orig)
Location and date: Pressburg (Bratislava), 11.03.1942
Summary statement: News of massacres of Jews in Russia committed by German SS.
With regard to the question contained in the latter part of the dispatch Number 9610/41 of 20 December 1941, I have the honour to communicate to Your Eminence that the Slovak authorities are by no means unfamiliar with the atrocities committed against Jews in occupied Russia. (1)
According to information provided by the Slovak military chaplain [Michael Buzalka], the massacres were committed by units of the militia “SS”, by order of the German government authorities. All the Jews of a given place were concentrated away from the town and murdered with machine guns.
(1) Cf ADSS 8.184, note 3.