Not that I am aware of.

The medieval county laws that specify what each free land-owning peasant should own (around 62% of the population, that owned about 52% of the arable land in the early 15th century) did not mention crossbows - instead bows and three dozen arrows were often required along with armour, sword or axe, spear, helmet and shield.

The bows were hunting weapons, and it seems like the peasants in Sweden started replacing their bows with crossbows in the late 14th century. These would be wooden hand-loaded crossbows initially used for hunting, not steel arbalests with wheelcrank loading systems.

That said, the vikings used longbow (although not quite as hard as English or Welsh longbows) style bows and could be quite skilled with them - most men could hunt with a bow. However, they never had the institutions the English kings built up to have large musters of longbowmen that could loose arrows in formation and indirectly.