As the latest Anonymous Monk did usefully say . . . from the point-of-view of your GUI application, the Perl script is simply an external program.   You simply need to build a command-line string containing the name of the script and any parameters, and execute that as you would any other external process.   If, as I expect, ActiveState has associated itself with the .pl filename extension, you ought to be able to just execute the script-file name.   (Naturally, you should start by fiddling-around with the proper way to do just-that within C#, until you get the necessary magic-spell just right.)

One issue, though, will be coming up with an appropriate way for your GUI application to wait for the external process (the Perl script) to complete, without hanging-up the user interface as GUI-programs must never do.   Of course the Internet should be filled with examples of how to do that part.   (“Don’t sweat it, don’t [re-]invent it, just google find it ...”)   It really does not matter that the external program in question is written in Perl or anything else.   Then, carefully look for any discussions on the Internet that may particularly relate to ActiveState-specific issues in this case.

Kindly observe that the external program (the script) will be a direct child-process of the GUI process:   it is not running under (Windows’s pathetic excuse for) a command-shell.