When ${\mathrm{CO}}_2$ is passed into $\mathrm{Ca}{\left(\mathrm{OH}\right)}_2$ a white precipitate is formed due to the formation of

$\mathrm{Ca}{\left(\mathrm{OH}\right)}_2+{\mathrm{CO}}_2\to {\mathrm{CaCO}}_3\downarrow +{\mathrm{H}}_2\mathrm{O}$

The white precipitate formed when carbon dioxide gas is passed into calcium hydroxide (lime water) is the calcium carbonate which turns lime water milky.

Hence, the white precipitate is ${\text{CaCO}}_3$.