Shared authentication between 2 websites with different user databases

I'm currently facing a lot of problems trying to integrate an existing C# application into a new Django project. The idea is to be able to use one user login to access the other website. Is there a way to do this?

I'm thinking of extending the Django built-in user model to contain login information for the other website, then automatically fill those fields in when the user accesses the C# website from within my Django app. Is there a better way of doing this?