Morality: Government vs. Church

Government can and should "legislate morality" in certain cases. I think everyone agrees that murder should be illegal.
The church (or any non-governmental) group should handle other morality issues because the government can't reach the heart of people. i.e. "Love your neighbor".
Some issues should be handled by both (murder) but all issues should be handled by the church -- the church should handle all moral issues and the government should also handle some of them.

The questions is: How do we decide which issues should be handled by the government and which should be left to the church? (The answer may vary by level of government but for this post I will consider all levels as one).

Questions that might help us answer the question:

• Is the issue easy to define and judge? (murder vs. hate)
• Does the issue affect the rights of other people?

I don't know the exact answer to this and I would appreciate your comments.