What periods and locations in European history had evidence based criminal trials? I'm interested in creating a medieval role playing setting and some fictional narratives involving crime investigators. However, some periods of early European history relied on trial by ordeal to determine innocence or guilt. Evidence appears to have little place in the proceedings. Do I need to go all the way back to ancient Greek and Roman courts? Do I need to go forward to the Renaissance? Perhaps there were a few medieval European cities with local legal systems that employed modern standards of evidence?
As heretical as this sounds . . . the Inquisition.
Of course this sounds completely counter-intuitive, as the crimes prosecuted by inquisitors were slippery, to say it mildly, and the "evidence" could be as ephemeral as cobwebs. However, it is precisely because of this that the Inquisition revolutionized the way trials were handled. Most of what we associate with a proper trial was either invented or popularized by the Inquisition. That includes proper trial transcripts, professional officers of the law, "modern" ideas of evidence, and limitations on torture.
(On the last point, understand that the common opinion of the time was that you could not trust a statement that wasn't made under torture. The manuals given to inquisitors are among the few documents of the era that instructed otherwise.)
There are several reasons why the Inquisition had such a tremendous impact on legal proceedings. The crimes being prosecuted were problematic for the conventional courts - the issues were often subtle and the verdicts often had major political and social ramifications. Many prosecutions involved difficult points of church doctrine, beyond the capacity of an ordinary feudal court to analyze. A verdict reached too casually could inflame a riot (or even a war ) - "heretic" and "rebel" were often all-but synonymous in a milieu where kings were assumed to be blessed by the divine. The Inquisition itself was extra-territorial, with avenues of appeal leading all the way to Rome.
Thus there was a lot of pressure on the inquisitors to develop iron-clad verdicts based on unimpeachable evidence, properly documented and derived in a consistent, professional manner. Of course, it took centuries to develop and was not always successful.
It should not be surprising that over time, the haphazard civil court systems of Europe would be deeply influenced by the much more sophisticated inquisitions. Standards for how courts were run, transcripts kept, appeals heard, and testimony obtained, inevitably improved in imitation of the evolving model. In time (mostly the 17th century) the law codes were updated to reflect the new procedures and the ideas that motivated them, and the form of our modern court systems were solidified.