Peruse has no advantage over read, and has the disadvantage that it gives a stiff old-fashioned air to a document:
I suggest therefore that you forward the correspondence I am enclosing to Mr. X so that he can peruse same and take the matter up.
"Read it" is more natural and friendly than " peruse same ". See also Same.
As a perusal of the Act will reveal . . .
Here again it is more natural and friendly to say "as you will see by looking at the Act".