Clark County's population was estimated to be 2,206 in the year 2006, a decrease of 179, or -7.5%, over the previous six years.
As of the U.S. Census in 2000, there were 2,390 people, 979 households, and 676 families residing in the county. The population density was 2 people per square mile (1/km²). There were 1,111 housing units at an average density of 1 per square mile (0/km²). The racial makeup of the county was 95.77% White, 0.25% Black or African American, 1.13% Native American, 0.08% Asian, 1.88% from other races, and 0.88% from two or more races. Hispanic or Latino of any race were 4.02% of the population.
There were 979 households out of which 30.20% had children under the age of 18 living with them, 60.30% were married couples living together, 6.20% had a female householder with no husband present, and 30.90% were non-families. 29.60% of all households were made up of individuals and 17.00% had someone living alone who was 65 years of age or older. The average household size was 2.39 and the average family size was 2.95.
In the county the population was spread out with 26.60% under the age of 18, 4.90% from 18 to 24, 23.10% from 25 to 44, 23.60% from 45 to 64, and 21.80% who were 65 years of age or older. The median age was 42 years. For every 100 females there were 95.60 males. For every 100 females age 18 and over, there were 88.50 males.
The median income for a household in the county was $33,857, and the median income for a family was $40,521. Males had a median income of $27,321 versus $20,833 for females. The per capita income for the county was $17,795. About 11.30% of families and 12.70% of the population were below the poverty line, including 18.00% of those under age 18 and 10.20% of those age 65 or over.