It is obvious for the detective that he is lying (and we as audience know it). But the detective needs a proof and depending on the local laws (that I am no expert in) she needs probably a strong suspicion and legal authority (e.g. by a judge or state attorney) for a search warrant. In-universe we have to believe that the detective either believed his story (no, she didn't), Bloom faked the videos so a forensic examination couldn't provide any information and he hid/encrypted the uncut videos (unlikely), or the detective couldn't claim a suspicion strong enough to get such warrant. It is not shown in the movie, after telling his story the detective makes clear that she doesn't believe it, then we see Bloom leaving the building.
I still wonder why the detective didn't mention the gaps in the videos. Bloom may have cut the beginning and end of the videos quite easily (e.g. the murderers driving away) but how would he explain phases of silence or missing seconds when his assistant talks dying or when the victim of the murder dies. But while this may be an indication of problems with his story it would still be the absence of proofs.
It's the rule of law and this seems to make the detective the only¹ moral person in the movie.
¹ We could discuss Frank.