According to the census of the year 2000, there were 2,747 people, 977 households, and 753 families in the town of Denmark. The population density was 54.3 people per square mile (21.0/km2). There were 1,149 housing units at an average density of 22.7 per square mile (8.8/km2). The racial makeup of the town was 96.76% White, 0.51% African American, 0.25% Native American, 0.18% Asian, 0.04% Pacific Islander, 0.84% from other races, and 1.42% of two or more races. Hispanic or Latino of any race were 1.82% of the population.