I agree that there was no rope at the crime scene. However, if there was any, it was likely removed from the area as the killer had also threw the mirror into the river to cover their tracks.

However, there are some contradictions in Zack's and Seraphina's accounts that need to be addressed, and I would suggest to any who choose to question them, to do so when they are separated from one another. As Miss Zange already mentioned - Zack claims Miss Nanami was bound up. Miss Seraphina denies this, stating that the dollhouse was too dark at the time for him to know for certain. Zack also agreed that the room was dark when he attacked them.

However, this calls into question why the dollhouse was dark in the first place. Given that Miss Seraphina had invited Miss Nanami to that location to examine a specific doll closely, one would naturally assume that the lights should have been on at the time. Of course, if that wasn't the intention at all... that would certainly clarify that mystery.