@minnseyare you sure? The command line git client which SourceTree is or is capable of using can handle client side SSL certificates since years. Please confirm this with your team.
Also see related tickets at:
Yes, Git does support it but we don't test Sourcetree with that configuration, so it may be that Sourcetree should work with it, i.e. rely on the underlying Git's configuration, but it may also be the case that Sourcetree is doing something to override the settings.
One thing you could check is to ensure that Sourcetree is using the same Git configuration by opening the Terminal in Sourcetree and using that to list it's view of the Git config.