Git bash tab completion for .sh files

I'm using msysgit on windows 7 and I found bash scripting very useful. I wrote some .sh scripts, but I'd like git bash to autocomplete their names. For now I can see, that after initial prompt git bash autocompletes only .exe, .bat and .com files. How can I allow autocompletion for .sh files?

Does bash have tab completion?

Bash completion is a functionality through which Bash helps users type their commands more quickly and easily. It does this by presenting possible options when users press the Tab key while typing a command.

How do I run a .sh file in Git?

downloaded "Git for Windows" (from https://git-scm.com/download/win). installed Git. to execute the . sh script just double-clicked the script file it started the execution of the script.

I found out that files with #!/bin/sh as first line are autocompleted. It's enough for me.