was there any case where the criminal actually fleed the sce

[TheBlind]

That depends. Do you mean a case where Conan knew who the culprit was but they escaped in the middle of his deduction? I don't think so. There have been cases when a culprit did flee the scene of his crime but it's due to Conan/Police not knowing all the details of the case yet or any reason to suspect the culprit. They are eventually brought back to the scene of the crime or somewhere similar due to the plot and Conan gets them there.

There have also been cases where Conan has let a criminal leave thinking he got away with it, in order to trap him. And of course there's the common case of the culprit trying to run after the deduction only to have pain inflicted on them.

[Schillok]

Makes me think about the first (or was it the second?) Detective Boy case. Where they found that code and followed the hints through Tokyo.
Well, they were not chasing a criminal at that time though... [Vol 4, File 7-10]

Or the 3rd Detective Boys case were Ayumi hid in the car trunk and the boys tried to follow her. [Vol 9, File 1-3]


There are a few cases where Conan is following some clues to reach a location.

[Abs.]

Volume 2, Files 4-7 (aka Files 13-16) re: the billion yen robbery would probably fit.  First they had to find the "father," then they had to find the "daughter."  Along the way they came across the first murderer... and then they finally caught up to the second murderer... but still in pursuit of the third murderer 

[djknitex]

There was the latest one... Two days with the culprit. Where at the beginning there was a murder and it takes 2 days to find out who it was.

[Abs.]

How about File 594, "The Fugitive"? 

[ccppfan]

One of the Metropolian Police Love Stories. XDD

In which Satou promises Shiratori that she will marry him if Tagaki doesn't come before sunset. :3

And "Shinichi" had to help Tagaki solve a case about a robbery. Before sunset.

Yeah, I loved that ep.

[NotSoFluent]

One of the Metropolian Police Love Stories. XDD

In which Satou promises Shiratori that she will marry him if Tagaki doesn't come before sunset. :3

And "Shinichi" had to help Tagaki solve a case about a robbery. Before sunset.

Yeah, I loved that ep.

Lol, that one was adorable.  I think it was in volumes #32 and #33.