dnd 5e – How much HP does a Pact of the Chain Imp familiar recover on a Short Rest?

I believe a Pact of the Chain Imp familiar uses the normal Imp stat block. So it has:

  • Hit Points 10 (3d4 + 3)
  • CON 13 (+1)
  • Challenge 1 (200 XP)

For purposes of recovering HP during a Short Rest, how many hit dice does the Imp have, and what dice does it roll?

Also, how is this determined, ie. how does this generalize to the other kinds of familiar?

I am asking this to get a RAW answer, if one can be found. I did not find any connection between monster HP and monster HD in my player books, and I am hoping the Monster Manual or DMG have something unambiguous.

My first guess, based on what I remember from some older editions of D&D, would have been that CR would be same as HD, but this does not make much sense when some of the 5e monsters have fractional CR.