Great first half, but it would've been so much scarier if (SPOILERS)
The movie delivers argubaly the most atmospheric, well acted and all-around scary first 40 minutes of a 2016 horror movie I've seen so far. Part of it is the initial lack of supernatural clichees and cheap jump scares. It's just a good setting for a horror movie, two characters doing their job and slowly realizing something is not right.
That brings me to my point - the movie kinda loses its touch once the rain of clichees starts pouring over the two main characters. The supposedly surprising reveal that he kills the girl and not the walking corpse was quite predictable, for example.
I think it would've been better if nothing about Jane Doe was revealed. And I mean literally nothing. They simply could've cut some of the jump scares and instead showed the characters losing their minds, having trouble seperating hallucinations from reality, like, say, 1408. It's ultimately what 'the witch' does to them, so why even reveal all that stuff? Are we supposed to feel sorry for the corpse? It proved completely uselees. They could've found out she is a demon or that her ghost is haunting them, it's just the usual old explanations that I wish horror movies would just stop serving on a silver platter, as if we the viewers are too dumb to appreciate a horror movie that doesn't completely fit within a sub-genre frame.
Overall, a pretty good horror movie that could've been the best of the year if they didn't get kinda sloppy with the supernatural elements and, at least to me, pointless background information.