Sponsored Topics. Crittenden is a city in Grant County, Kentucky, United States. The population was 2,401 at the 2000 census. Crittenden is located at 38°46′56″N 84°36′21″W / 38.78222°N 84.60583°W / 38.78222; -84.60583 (38.782248, -84.605794).