As Google Code doesn't support Git, I'm moving a Google Code hosted project to my own server. And change to use JIRA for issue tracking, because there is a Git plugin for JIRA. (I don't like the Git plugin for Trac, though) It's easy to convert SVN repository to Git, however, unfortunately, Google Code seems not able to export the issue database. So this question.
You can get issues out of the issue tracker in two ways:
For your needs, you probably want the GData API.
But, as mentioned by @Sathya, Google Code supports git.