You need to give more information. Are there two different reservations? Do you have any status? What's the booking class? Is your trip starting from JFK?
Singapore Airlines has an interline baggage agreement with SAS allowing for baggage to be tagged across different flight reservations. I've had to explain the process to the check-in people sometimes. It is not a combination of PNR, just tagging of baggage to final destination.
You might also be able to through check-in to your SAS flights if it is ticketed with Singapore Airlines.
See here:
If you are travelling on a Singapore Airlines operated flight and connecting to any of the below carriers, you will be able to perform a through check-in for both flights, provided that the booking is on a Singapore Airlines ticket.
However, if your journey begins with any of the following carrier and connecting to a Singapore Airlines flight, you may wish to check with that carrier directly.