Yes, they did. The height of recorded activity, is precisely because the printing press had arrived after the 1400's, to allow records.
Well, actually, yes... but, no.
The printing press did play a big role in the witch panic, but not in the keeping of records. Records weren't kept by printed books, but by hand. And that was true up to very recently. Printing allows for distributing books, which you don't really need to do for "records".
The truth is in the middle ages they didn't really burn witches, and the Catholic Church had issued decrees banning the practice of killing witches early on in the middle ages. There also just weren't many people in the middle ages that believed in witches.
The role the printing press had in the witch panic is it allowed self-described 'experts' to print books decrying witches and describing witches, and then to widely disseminate those books. It's books that caused the panic and caused people to begin to imagine that they were surrounded by witches making pacts with the devil. And it's worth noting that where those books made inroads was mostly in the North of Europe, which at the time was no longer dominated by a single religious institution.
Incidentally, the medievals were also cleaner than the Europeans of the early modern period. Europeans didn't stop taking baths until after the Black Death closed all the public baths.
And Joan of Arc wasn't burned for wearing women's clothing either. That was the official excuse. She was actually burned because she'd embarrassed a lot of people in a position of power, and they need some official excuse to murder her. Similar thinking went into book burning. In most cases, they didn't burn all the books. They kept copies of the books in, as it were, 'the restricted section of the library'. The authorities in power weren't afraid of books. They were afraid of not being able to control public opinion.
And in general, I rather think your simple line downward from the classical era to the medieval one is a... overly simplistic one. For just one example, you ought to read some about the practice of exposing female infants to the elements to die, a practice that was rather successfully squashed by those same medievals you abhor.