Hello Rajeev,
it depends on what your constructor does: if the constructor opens a file or worse connects to a DB or does anything that might go wrong, then yes, you have to check if the INSTANCE is null or not (and catch any exception) and if it is
you should fall back to a default (sometimes dummy) alternative.
If you are not doing anything critical then I always felt comfortable skipping that check.
In my experience, with a PropertyManager Singleton, I usually had to read te properties from a file, but if the file was not there, I never returned null but instead I logged the issue and used a default PropertyManager with default values.
I believe this brings more robust code and it is a neater design.
Just my 2 cents!
Giovanni