I stumbled upon this reading "Roskilde Bys historie 1536-1850". A book published by the Historical Society of Roskilde and Roskilde museum.
The quote is as follows "Tilmed havde byen den tvivlsomme fornøjelse at huse Carl Gustavs fjerne allierede: gesandterne fra khanen over tatarerne på Krim samt bidrage til at udruste et helt kompagni tatarer med sabler, pistoler og hylstre dertil (120 rdl.)."
My own translation "Beyond this, the town had the dubious pleasure of quartering Carl Gustavs distant allies, the offices of the Khan of the Tatars of Krim, as well as paying for the armament of an entire company of Tatars with sables, pistols, and pistolsholders (to the cost of 120 rigsdadler)".
The quote is in the context of the expenses that Roskilde endured as part of the Swedish occupation during the Carl Gustav Wars. I can't seem to wrap my head around how and why the Swedish King managed to ally himself with the Tatars, and bring them to Denmark. I can't find a primary source, though the mention of a price makes it seem that it comes from some kind of bookkeeping. What were they doing in Roskilde, how did the alliance come about, are there other sources of their interaction with the Danes and Swedes?
Crimean Tatars were definitely involved in the 2nd Northern War, though as Swedish foes rather than enemies. In 1656, 2000 of them fought with the Polish-Lithuanian forces in Poland and ended up raiding Eastern Prussia. However, as an organized force they went home later that year.
Another group of Tatars attacked Swedish Ally, Duke George Rakoczy of Transylvania, in Southern Poland (modern Ukraine) in 1657.
It's possible that some members of that groups could have stayed on and even switched sides later (which wouldn't be uncommon at the time), but that would be speculation on my part.