Well, since Conan's fingerprints are on his cellphone, Shinichi's are as well. Takagi took the cell phone to check if the person who died has his fingerprints on it (Akai). Takagi could have found that Conan and Shinichi's finger prints match.
Wow, Shin-chan!! You already have a new one. I'm impressed. This one is... Interesting. Let's see...
I was also wondering this: How long did it take to drive back to the apartment from the business trip and what the time was the body discovered at?