The TortoiseGit installer comes as an MSI file, which means you should have no problems adding that MSI file to the group policies of your domain controller.

A good walk-through on how to do that can be found from Microsoft: https://learn.microsoft.com/en-us/troubleshoot/windows-server/group-policy/use-group-policy-to-install-software .

Versions 0.3.0 and later of TortoiseGit must be installed under Computer Configuration and not under User Configuration. This is because those versions need the new CRT and MFC DLLs, which can only be deployed per computer and not per user. If you really must install TortoiseGit on a per user basis, then you must first install the MFC and CRT package version 11 from Microsoft on each computer you want to install TortoiseGit as per user.

You can provide a default setting for the SSH client in HKLM\TortoiseGit\SSH.

TortoiseGit automatically finds git.exe if a normal msysGit/Git for Windows installation is on the computer or git.exe is on the PATH (and is runnable in a normal cmd.exe session - you might need to also put the [MSYSGIT INSTALLDIR]\mingw\bin on the PATH if you use the msysGit development package).

For completely disabling automatic update checking see VersionCheck in the section called “Advanced Settings”.