We know for certain that Mandrake leaves were used in a variety of potions...
He, Ron and Hermione sat in the library as the sun set outside,
tearing feverishly through page after page of spells, hidden from each
other by the massive piles of books on the desk in front of each of
them. Harry’s heart gave a huge leap every time he saw the word
‘water’ on a page, but more often than not it was merely ‘Take two
pints of water, half a pound of shredded mandrake leaves and a newt
Harry potter and the Goblet of Fire
...and other magics...
For the space of one entire month (from full moon to full moon), a
single leaf from a Mandrake must be carried constantly in the mouth.
The leaf must not be swallowed or taken out of the mouth at any point.
If the leaf is removed from the mouth, the process must be started
Short Stories from Hogwarts of Heroism, Hardship and Dangerous Hobbies
But the only specific reference that the root was used in the restorative draught seems to come from the Gameboy Color game (where you need to collect "Mandrake Root" in order to finish the potion and complete the level) and the Harry Potter and the Half-Blood Prince video game where Harry comments
"Stewed Mandrake. Much quieter than the live version."
That all being said, the implication is very very clear. It's the root that's used, not just the leaves.
‘We will be able to cure her, Argus,’ said Dumbledore patiently.
‘Professor Sprout recently managed to procure some Mandrakes. As soon
as they have reached their full size, I will have a potion made which
will revive Mrs Norris.’
Harry Potter and the Chamber of Secrets