Introduction:
Kathak is one of the major classical dance forms of India. It is known for its intricate footwork, graceful movements, and expressive storytelling. Kathak originated in the northern part of India and is associated with the state of Uttar Pradesh.

Explanation:

1. Uttar Pradesh:
- Uttar Pradesh, a state in northern India, is widely recognized as the birthplace and stronghold of Kathak.
- The historical city of Lucknow, the capital of Uttar Pradesh, is particularly known for its rich Kathak tradition.
- The Lucknow gharana (school) of Kathak, also called the Lucknow style, evolved in this region and has made significant contributions to the dance form.

2. Tamil Nadu:
- Tamil Nadu, located in the southern part of India, is known for its classical dance form called Bharatanatyam.
- Bharatanatyam originated in the temples of Tamil Nadu and has its own distinct style and repertoire.

3. Maharashtra:
- Maharashtra, located in western India, is associated with the classical dance form called Lavani.
- Lavani is a vibrant and energetic dance form known for its rhythmic movements and folk elements.

4. Gujarat:
- Gujarat, also located in western India, is known for its folk dance forms such as Garba and Dandiya Raas.
- Garba and Dandiya Raas are performed during the Navratri festival and involve lively, circular movements.

Conclusion:
Based on the information provided, the state associated with the classical dance form Kathak is Uttar Pradesh. Kathak originated in Uttar Pradesh, particularly in the city of Lucknow, and has a rich tradition in this region.