That really isn't clear from a single verse that can be read in both a corporate and an individual way taking the elder (priest) as representative of the congregation.
"Is any among you afflicted? let him pray. Is any merry? let him sing psalms. Is any sick among you? let him call for the elders of the church; and let them pray over him, anointing him with oil in the name of the Lord: And the prayer of faith shall save the sick, and the Lord shall raise him up; and if he have committed sins, they shall be forgiven him. Confess your faults one to another, and pray one for another, that ye may be healed. The effectual fervent prayer of a righteous man availeth much."
James 5:13-16 KJV
The Lord said,
"Moreover if thy brother shall trespass against thee, go and tell him his fault between thee and him alone: if he shall hear thee, thou hast gained thy brother. But if he will not hear thee, then take with thee one or two more, that in the mouth of two or three witnesses every word may be established. And if he shall neglect to hear them, tell it unto the church: but if he neglect to hear the church, let him be unto thee as an heathen man and a publican. Verily I say unto you, Whatsoever ye shall bind on earth shall be bound in heaven: and whatsoever ye shall loose on earth shall be loosed in heaven. Again I say unto you, That if two of you shall agree on earth as touching any thing that they shall ask, it shall be done for them of my Father which is in heaven. For where two or three are gathered together in my name, there am I in the midst of them."
Matthew 18:15-20 KJV
And though one could argue that this passage relates only to a subset of sins (those between one human and another) a Catholic is likely to see and understand the principle at work here as applicable to all sins and the way to confess them.
Penance is a disciplinary measure and as such has always been in the hands of the bishops to decide.