Personally, I would have the developers build release scripts for applying to the Test environment then hand them over with release notes to the DBA.

He then handles the release process, ensuring he has a back up of the database PRE deployment incase of errors. You also get to test the scripts properly before they get sent to the Production DB

Finally you also have an audit trail of what was released and when, and you know what state each environment is in, and if any issues are down to scripts.