Crittenden is a home rule-class city in Grant and Kenton counties, Kentucky, in the United States. The population was 4,023 as of the 2…Crittenden is a home rule-class city in Grant and Kenton counties, Kentucky, in the United States. The population was 4,023 as of the 2020 Census, up from 3,815 as of the 2010 census, which was further up from 2,401 at the 2000 census.