A reminder that sounds like a threat
It's the third time you've asked for the form. You're right to be annoyed. You also still need the form.
You typed
As I said in my last two emails, I still need the signed form. I can't do anything until you send it. Please send it today.
You asked: Professional tone.
Reads as irritated. "As I said in my last two emails" tells the reader they are being blamed, and "Please send it today" lands as an order.
Hi [name], I'm still missing the signed form, and I can't move this forward without it. Could you send it over today? If something is holding it up on your side, let me know and I'll help sort it out. Thanks, [your name]
