Bark Crab Spiders in the genus Bassaniana and those in the genus Coriarachne are very similar to one another so it made sense to cover them together. Both are in the Family Thomisidae (the crab spiders). Both are commonly found on the trunks of trees in forested ecosystems where their cryptic coloration helps them to blend in. They typically overwinter beneath bark or in the leaf litter as either adults or penultimates (1 molt away from adulthood) (Bowling & Sauer, 1975).

The characteristic that helps distinguish these crab spiders from other cryptically-colored members of the family (Ozyptila/Xysticus) is the very flattened shape of the carapace. Bowling & Sauer also indicates that the anterior eye row is either straight (Coriarachne) or slightly recurved (Bassaniana)(1975).

There are two species of Bassaniana found in Minnesota and distinguishing between them is extremely difficult without microscopic examination (and even with dissection in some cases). Additionally, I have found a paper that suggests that hybrids may occur (B. utahensis x versicolor) or at least that some individuals are too close to call (Jennings & Cutler, 1996). Identification from habitus images alone should be done with caution and most individuals should probably be identified only to the genus level. Both species likely have a statewide distribution though their distributions are poorly known at this time (9 counties each).

I have voucher images for female B. utahensis or Utah Crab Spider. Assume that females of the other species are similar.
https://www.inaturalist.org/observations/14326116
https://www.inaturalist.org/observations/54703865

I have voucher images for male B. versicolor or Multicolored Bark Crab Spider. Again, assume that males of the other species are similar.
https://www.inaturalist.org/observations/6737829
https://www.inaturalist.org/observations/86277486

While there are no known records of Coriarachne brunneipes in Minnesota, this species occurs on the state list as hypothetical. Its known distribution extends from Ontario westward in Canada and south into the mountainous western U.S. (Bowling & Sauer, 1975). I expect it will be found in northern Minnesota at some point. Bowling & Sauer indicate that this species has a more uniform color (pattern?) than the Bassaniana species listed above (1975). I found only one voucher image of a male online on BugGuide: https://bugguide.net/node/view/727756/bgimage.

Happy spidering!

Sources
•Bowling, T. A. & R. J. Sauer. 1975. A taxonomic revision of the crab spider genus Coriarachne (Araneida, Thomisidae) for North America north of Mexcio. Journal of Arachnology, 2:183-193.

•Jennings, Daniel & Bruce Cutler. 1996. Crab spiders (Araneae: Philodromidae, Thomisidae) of Ramsey County, Minnesota. General Technical Report NC-185. St. Paul, MN: U.S. Department of Agriculture, Forest Service, North Central Forest Experiment Station. 35 pages.