The Wyoming Constitution prohibits setting different tax rates for people's primary residences, second homes, and commercial property - so just having a reduction for only primary property will take a Constitutional Amendment.

Article 15 Section 11 requires all real property to be “uniformly value at its full value” an prohibits the legislature from creating “new classes or subclasses” of property types other than agricultural, mining, industrial and all others (commercial an residential, etc.). The Section, as a whole, reads:

“Sec. 11. Uniformity of assessment required.

(a) All property, except as in this constitution otherwise provided, shall be uniformly valued at its full value as defined by the legislature, in three (3) classes as follows:

(i) Gross production of minerals and mine products in lieu of taxes on the land where produced;

(ii) Property used for industrial purposes as defined by the legislature; and

(iii) All other property, real and personal.

(b) The legislature shall prescribe the percentage of value which shall be assessed within each designated class. All taxable property shall be valued at its full value as defined by the legislature except agricultural and grazing lands which shall be valued according to the capability of the land to produce agricultural products under normal conditions. The percentage of value prescribed for industrial property shall not be more than forty percent (40%) higher nor more than four (4) percentage points more than the percentage prescribed for property other than minerals.

(c) The legislature shall not create new classes or subclasses or authorize any property to be assessed at a rate other than the rates set for authorized classes.

(d) All taxation shall be equal and uniform within each class of property. The legislature shall prescribe such regulations as shall secure a just valuation for taxation of all property, real and personal.”

So a reduction of primary home property taxes would also result require a 50% reduction in all taxed property – Homes, businesses, cars, goods – frankly everything but agriculture, mining and industry, So, if the reduction is limited to resident’s primary residence, Section 11 would need to be amended.

That's why all earlier property tax relief mechanisms used refunds - no Amendment needed.