I don't know if Utah has one or not. They had Senate Bill 60 to create a program similar to Colorado's. I can only find mention of it from 2010 and nothing saying that it exists. Utah does use part of Hunting and Fishing license fees to go to a general fund for S&R reimbursement. So you could always purchase one of those. I don't know the coverage it offers, such as you are off the hook for S&R costs if your or my dumb ass needs them.
Keep in mind the S&R card in Colorado only covers you for the S&R portion of the costs. Flight for Life, ambulance, law enforcement agencies that get involved can also get you a bill.
Anyway, from what I can find, looks like it didn't pass. Not sure though. Your local outdoor retailer will probably know if a USAR card exists or not.