Luke1:5 and his wife was of the daughters of Aaron, and her name was Elisabeth.
At least one of Mary's parents, then was also a full-blooded Levite.
I can live with this if the full-blooded Levite is her mother. Quick consult the pro-evangel? :-)
I took a look at it, but it doesn't provide any further information. I did turn up some Orthodox sources which reported a tradition that Mary's father Joachim was a Levite, but I have been unable to find an original source for the claim.