Step 1: Understanding the Concept:
The question asks to identify a specific treatise on dance that originates from or focuses on the region of Rajasthan.
Step 2: Detailed Explanation:
Let's analyze the given texts:
1. Nrttyaratnāvalī: This is a comprehensive text on dance authored by Jayapa Senani in the 13th century. He was a military commander under the Kakatiya rulers of Warangal (in modern-day Telangana). The text primarily describes the dance forms of the Deccan region.
2. Govind Sangīta Līlā: While sounding plausible due to the connection of 'Govind' (Krishna) with Rajasthan, this is not a well-known standard treatise on Rajasthani dance.
3. Nṛtyaratnakośa: This is a significant work on dance and music authored by the learned ruler Maharana Kumbha of Mewar (Rajasthan) in the 15th century. It is an authoritative text that details the regional dance practices of its time and is a vital source for the history of dance in Rajasthan.
4. Hastamuktāvalī: This is a text focusing specifically on hand gestures (\textit{hastas} or \textit{mudras}) in dance. It is particularly associated with the classical dance traditions of Assam and is attributed to Subhankara Kavi.
Step 3: Final Answer:
The Nṛtyaratnakośa by Maharana Kumbha is the important manual on dance from Rajasthan among the given options. Therefore, option (3) is the correct answer.