On the day of the killing, she just happened to wander into the lab.

It probably felt like going for a walk without any real thought or intention.

She can hide her presence, so the kappa didn't notice her.

That being said, we know she didn't enter the heavily secured second floor. Her ability doesn't work on machines without a consciousness, after all.

And yet, Reisen, with her special eyes, was able to see Koishi.

She saw her in the boiler room, left the cleaning to me and headed over.

Only Reisen knows what happened at this point.

But Koishi wasn't actually looking at her, reading the notice board instead.

Suddenly, Koishi's arm swung up and stabbed the screwdriver through Reisen's neck.

There's no explanation for why that happened.

Just like you can't explain why you bite your nails, or why you forget where you put something, Koishi's body was just following a random impulse. There is no motive.

People like us absolutely couldn't "just happen" to kill someone. We're restrained by consciousness and reason.

Koishi has no such thing.

Conversely, she is the one and only being who could kill another "for no reason".