${\mathrm{CO}}_3^{2-}$ and ${\mathrm{HCO}}_3^{-}$  can be distinguished by :

It is possible to differentiate between sodium carbonate and sodium bicarbonate aqueous solutions using the phenolphthalein indicator. The aqueous solution of sodium carbonate with phenolphthalein indicator is pink in colour. While the aqueous solution of sodium bicarbonate is colourless.

Hence, the correct option is A.