Although I don't know what's going on behind the scenes, as it may be hiding the command window as described above, but you could look into using Perl2exe and compile your script using the -gui option. The documentation states using the -gui option will:

Create a no-console executable. This can be used for Tk and Win32::GUI applications. I/O to STDOUT and STDIN will not be visible. Applies to Win32 version only.

I've tried it and it seems to work as advertised.

"Make everything as simple as possible, but not simpler." -- Albert Einstein