In the first episode when Aunt Bee replaces Rose Barney tells Andy that he's glad that he was hired on as Deputy because he thinks he's the right man for the job. He then says I want to thank you cousin Andy.
Wish they had explained exactly how they were kin. We missed a great chance to find out when Andy and Barney were discussing Barney's anniversary gift to his parents (septic tank). If only Andy had called them "Aunt" and "Uncle" So-and-So. That might have given us a clue.
It is like this. You needed a lot of hands to work on the farm. My father is one of 15 childten (13 that lived), as was his father, as was his father..give or take. My kin live all over the country and if they aren't an aunt or uncle they are just cousin. My first cousin has a grandson with my first and last name (pretty good ball player too). We don't try to figure out if he is 3rd cousin 4 times removed or what, he is just cousin to me. So in a way, I am my own cousin!
Andy and Barney are mentioned as cousins in three episodes. Episode 1 (This is mentioned as Barney and Andy are standing by the truck that Andy is washing. It is also mentioned in Episode 2 and 6, so that makes three in all!