No, you cannot see who screenshots your Instagram Close Friends story. Instagram does not provide any notification or feature that allows users to see who has taken a screenshot of their stories, including those shared with their Close Friends list.
This is consistent with Instagram's general policy of not notifying users about screenshots of their content. This policy applies to all types of stories, including regular stories, live stories, and even direct messages.
While there are third-party apps that claim to offer screenshot notifications, these apps are often unreliable and can compromise your account security. It's best to rely on Instagram's built-in features and avoid using third-party apps that require access to your account.