Close it is correct.

I'd understand this as literally putting the book down - putting it down on the table or on your desk. Or in other words, to stop reading it. We often use the phrase 'put down' to talk about a book in the sense of taking a break from reading it. When we describe a story which is so exciting that you can't stop reading it, we very often use the phrase 'I couldn't put it down!'.

Probably better to say, you can/should put your book down anytime, and have an emotional break. When you feel like it, take a break from reading.