How was the Sword of Gryffindor placed into the pool in the Forest of Dean in Deathly Hallows?

‘So how did the sword get in that pool?’

‘Whoever cast the Patronus must have put it there.’

They both looked at the ornate silver sword, its rubied hilt glinting a little in the light from Hermione’s wand.

Deathly Hallows - page 304 - UK - chapter 19, The Silver Doe

I've read the chapters The Silver Doe (DH) and The Prince's Tale (HBP) many times over and I'm still not certain whether Snape placed the Sword of Gryffindor in the pool in the Forest of Dean, or if he somehow managed to have his doe Patronus place the sword there.

Was it Snape or his Patronus that actually placed the sword in the pool?