Step 1: Identify the Objective: The inquiry seeks to pinpoint a dance treatise originating from or pertaining to the Rajasthan region.
Step 2: Analyze Options:
1. Nrttyaratnāvalī: Authored by Jayapa Senani in the 13th century, this text covers dance forms of the Deccan region.
2. Govind Sangīta Līlā: While the name suggests a Rajasthan connection, it is not a recognized treatise on Rajasthani dance.
3. Nṛtyaratnakośa: This 15th-century work by Maharana Kumbha of Mewar (Rajasthan) is a significant source detailing regional dance practices and is crucial for understanding Rajasthani dance history.
4. Hastamuktāvalī: This treatise focuses on hand gestures (\textit{hastas} or \textit{mudras}) in dance and is linked to Assamese classical dance traditions.
Step 3: Conclude: The Nṛtyaratnakośa by Maharana Kumbha stands out as the relevant Rajasthani dance manual among the provided choices. Hence, option (3) is the correct selection.