76-10-504. Carrying concealed dangerous weapon -- Penalties.
(1) Except as provided in Section 76-10-503 and in Subsections (2) and (3):
(a) a person who carries a concealed dangerous weapon, as defined in Section 76-10-501, which is not a firearm on his person or one that is readily accessible for immediate use which is not securely encased, as defined in this part, in a place other than his residence, property, or business under his control is guilty of a class B misdemeanor; and
76-10-511. Possession of loaded weapon at residence authorized.
Except for persons described in Section 76-10-503, a person may have a loaded firearm at his place of residence, including any temporary residence or camp.
From the Utah code above you are OK in your house, and the surrounding property that is yours. A rented house is considered, for purposes such as this, as your property if your name is actually on a lease or rental agreement. In a duplex, triplex, apartment complex, probably the only part of the property considered as "yours" is the actual residence itself, I don't think the surrounding property in that case would be considered yours.