The UVic Writer's Guide

"The man who mistook his wife for a hat"

Use which for things:

("The house which you are thinking of robbing").

That can refer to either:

"The man that mistook his wife for a hat,"

"The house that you are thinking of robbing."

Note that if the subject of the subordinate clause is different from that of the main clause, you can often omit the relative pronoun:

"The house you are thinking of robbing is empty,"

But:

"The house that was broken into was empty."