What is the definition of primary residence in US law?

[larry]

When a family from Europe, where they have their primary residence, invest for a holiday home in the US without any mortgage and keep the unit without renting it out, but use it exclusively for their holidays for 2/3 months in each year, why the County concerned should refuse to entertain the application of Homestead Exemption on Propert Tax, for the reason that the primary residence is not in the US. Of-course it may the Law and rules of the Country/County; but is it reasonable?