NRS 450.625
Trustees of district that includes territory within more than one county.
1.
If a hospital district created pursuant to NRS 450.550 to 450.750, inclusive, includes territory within more than one county, the board of trustees of the hospital district must consist of three members of the board of county commissioners that created the district and:(a)
Three members of the board of county commissioners of each county other than the county of the board of county commissioners that created the district, if the portion of the county included in the district is two-thirds or more of the total area of the county;(b)
Two members of the board of county commissioners of each county other than the county of the board of county commissioners that created the district, if the portion of the county included in the district is more than one-third of the total area of the county but less than two-thirds of the total area of the county; or(c)
One member of the board of county commissioners of each county other than the county of the board of county commissioners that created the district, if the portion of the county included in the district is one-third or less of the total amount of the area of the county.2.
Each member of the board of trustees appointed pursuant to this section must be appointed by the board of county commissioners of which he or she is a member.3.
The term of office of the members of the board of trustees is 3 years.4.
A member who ceases to be a member of the board of county commissioners that appointed him or her ceases to be a member of the board of trustees.5.
Any vacancy must be filled for the unexpired term by the board of county commissioners that appointed the member who created the vacancy.
Source:
Section 450.625 — Trustees of district that includes territory within more than one county., https://www.leg.state.nv.us/NRS/NRS-450.html#NRS450Sec625.