I recently got a Logitech keyboard case for my iPad. The thing works fine, but what was very annoying is that the iOS password autofill is not working when the external keyboard case is connected. It simply does not suggest usernames and passwords for sites where you have saved them in your keychain.
This is probably a security feature, but you can use the following workaround to access your saved usernames and passwords: go to Settings, General, Keyboards and activate the option Shortcuts.
Whenever you visit a logon page now for which you have saved your password, a small bar will appear at the bottom of your screen, with a Passwords button. Tap the button to access your saved passwords.