William and Mary OOS female

What are my chances of getting into William and Mary as a NC resident, with a 1380 SAT and 31 ACT?

you can refer to the W&M common data set to see the profile of admitted students:
http://www.wm.edu/offices/ir/documents/cds/cds1617_part_c.pdf
looks like 31/1380 is around the middle of the range.
So likely your chance is right around the acceptance rate for OOS applicants in general, which is lower than the overall acc rate (http://www.wm.edu/admission/undergraduateadmission/facts-figures/admission-stats/index.php)