There are three Rites of Reconciliation
1. Rite for the Reconciliation of Individual Penitents.
2. Rite for Reconciliation of Several Penitents with Individual Confession and Absolution.
3. Rite for Reconciliation with General Confession and Absolution.
I don't know much about the second and third forms as the second is rarely celebrated here and the third is forbidden throughout Australia. I see no problem with a non-Catholic attending the service, but the actual confession and absolution is another matter.
From the Code of Canon Law
Can. 844 §1. Catholic ministers administer the sacraments licitly to Catholic members of the Christian faithful alone, who likewise receive them licitly from Catholic ministers alone, without prejudice to the prescripts of §§2, 3, and 4 of this canon, and ⇒ can. 861, §2.http://www.vatican.va/archive/ENG1104/__P2T.HTM
§2. Whenever necessity requires it or true spiritual advantage suggests it, and provided that danger of error or of indifferentism is avoided, the Christian faithful for whom it is physically or morally impossible to approach a Catholic minister are permitted to receive the sacraments of penance, Eucharist, and anointing of the sick from non-Catholic ministers in whose Churches these sacraments are valid.
§3. Catholic ministers administer the sacraments of penance, Eucharist, and anointing of the sick licitly to members of Eastern Churches which do not have full communion with the Catholic Church if they seek such on their own accord and are properly disposed. This is also valid for members of other Churches which in the judgment of the Apostolic See are in the same condition in regard to the sacraments as these Eastern Churches.
§4. If the danger of death is present or if, in the judgment of the diocesan bishop or conference of bishops, some other grave necessity urges it, Catholic ministers administer these same sacraments licitly also to other Christians not having full communion with the Catholic Church, who cannot approach a minister of their own community and who seek such on their own accord, provided that they manifest Catholic faith in respect to these sacraments and are properly disposed.
§5. For the cases mentioned in §§2, 3, and 4, the diocesan bishop or conference of bishops is not to issue general norms except after consultation at least with the local competent authority of the interested non-Catholic Church or community.