The hands must be unified to ensure a sound putting stroke. That’s why the grip is all-important.
Regardless of how you hold the club – with a reverse-overlap or 10-finger grip, for example – the palms should face each other directly. Check this by taking your normal putting grip, then unlocking both hands so they’re flat against either side of the handle. Are your palms parallel?
A good way to get the feel for a palms-facing grip is with a standard ruler. Hold it between your hands, both palms flat against the sides, then curl the fingers around the ruler as though it were a putter.
When the hands are in harmony, your putting stroke will be too.