It is my understanding that if you confess to killing your neighbor in confession, it will be suggested that you come back for absolution after you have confessed to the police.
Of course I've never killed my neighbor, so I don't know for sure. Perhaps there is a liberal democrat out there who could give us a difinative answer.
I believe you are describing what is supposed to happen if you confess to your priest according to the Roman Catholic tradition.
I was referring to a more general instance where someone repents to Christ (directly or via His Church). Without that repentance, there cannot be forgiveness.