Here are various Singer models and how to locate their serial numbers.

1 1/2 Litre Number Locations This is for the 1.5 Litre 4-Seater Sports but it should be the same for others. 

Le Mans Number Locations Also, known as the Singer Nine or 9HP 

4A Serial Number Locations The Singer 4A 

4AD Serials. The Singer 4AD, the most common Singer in the U.S. Your car is most likely one of these. 

Gazelle serial number locations.

Once you find your serial number, visit this page on how to properly date the year of manufacture of your Singer (Sorry to say the DMV registration papers are frequently wrong, cars were frequently registered based on the first year sold, rather than model year)