This came off the Utah Division of Water Rights homepage:
"Rainwater harvesting is now legal in the state of Utah, starting May 11 2010. Senate Bill 32 was approved in the 2010 session that provides for the collection and use of precipitation without obtaining a water right after registering on the Division of Water Rights web site.
There is no charge for registration.
Storage is limited to one underground 2500 gallon container or two above ground 100 gallon containers. Collection and use are limited to the same parcel of land owned or leased by the rainwater collector."
On the site there is a link to register and it takes seriously 2-5 minutes to fill out the info, then they redirect to where you can print out a certificate for your records. It looks pretty snazzy with all of my other documents.