Got Murder? - S3-E12
Continuity mistake: When Catherine is looking through the contents of the birds nest, she takes out the teething ring and places it on a pile on the left. When Gil comes in and asks her what she has, the shot shows the nest and the teething ring is back in it.
Answer: The episode on CSI:NY was called "Love Runs Cold" and first aired on October 4, 2006 (Season 3, Episode 3) and involves the investigation of a model found stabbed to death by an ice dagger.
OneHappyHusky