Most likely he lied about the warrant, he had no real evidence a judge won't just him the warrant without some type evince. Plus pretty sure you're suppose to have the warrant present and I saw no type of paper with him.
But then whatever evidence he got from using the (fake) warrant would be useless in court, the whole investigation would be for nothing, and he would def lose his job. Also, he used help from other police officers in searching the Clinic, which shows that, even if he was bluffing, he would have had to create a fake document to at least give to his boss... sounds a lot of work but then again: that detective IS a bastard.
You're right it wouldn't hold up in court. How did he think this was going to work. ┑(￣Д ￣)┍
I know I am asking a bit too much of realism in a manhwa about literal vampires and demons, but I wonder how the detective got a warrant for Deok. I mean, they literally have no evidences of his involvement in the murders; the only thing they got is something strange the detective saw once in a totally unrelated night to the murders. What a mess of Law System, Deok doesn't deserve this ヽ(`Д´)ﾉ