If you're looking for manga similar to Dispatch!!, you might like these titles. All recommendations are made by Anime-Planet users like you!
Eiji is a teenager who's rough and rude and loves to fight. However Eiji has a strange power; when he comes in contact of certain objects, he can see memories contained within the objects themselves. When he finds himself involved in a dark murder case, he assists a beautiful young profiler to find the murderer. Afterwards, she continues to ask for his assistance in more complex investigations.
If you got fooled into believing that Dispatch!! is actually a detective manga by the first 4 translated chapters (which it is not, because it is a H manga) and now you want to read a manga with strong female lead who also happens to be a police detective, then you ought to read Psychometrer Eiji.
Ryoko Yakushiji is the gifted and beautiful Superintendent of the Tokyo Metropolitan Police; no matter what the problem – science gone wrong or supernatural monsters – it seems there is nothing she cannot solve. With her new partner, the mild mannered Junichiro Izumida, she sets about tackling some of Tokyo's most terrible crimes. However, as Izumida quickly discovers, Ryoko's talent comes with a big ego and some strange personal baggage; cleaning up the streets of Tokyo becomes not just a matter of finding the bad guys, but trying to survive Ryoko's attitude problem as well!
The first 4 chapters of Dispatch!! are very similar to Yakushiji Ryouko no Kaiki Jikenbo, so if you want more of female + male detective due you should go read Yakushiji Ryouko no Kaiki Jikenbo right now. As for the rest of Dispatch!!, you'd better of staying as far away from it as you can...