In American usage, "welch" seems to be the more common word meaning to renege on a bet; while "Welsh" refers to the people or their ethnicity. Here's a link that will entertain you for hours:

http://english.stackexchange.com/questions/72806/are-the-terms-welsh-or-welch-as-in-reneging-on-a-bet-derogatory-toward-the

-Joe-