Well,, I am sticking with the 1940`s era !! You didn`t say how the top drawers were joined and how a piece is made is a large part of determining the era made !!
I am not entirely sure this is a factory piece or made by a local cabinet maker !! It is vaguely in the Chippendale style but the appliques would not have been used on the factory reproductions !! The pulls are nice quality and may have been taken from another piece to use on this one !!