The Irish Deaf Society has sought a meeting with Cardinal Connell to outline its unhappiness with the Catholic Chaplaincy for the Deaf.
There has been friction between some IDS members and the chaplaincy for some time. However, the National Association for Deaf People (NADP) has disassociated itself from the dispute, saying that it has "absolutely no complaints" with the chaplaincy, which ministers to the spiritual needs of deaf people.
The IDS has accused the chaplaincy of becoming "over-involved" in private religious ceremonies, regardless of the wishes of the deaf person.
A spokesman for the Chaplaincy for the Deaf said he did not want to comment on the matter or to be drawn into battle with the organisation. However, it is understood that the chaplaincy has strongly rejected the criticism and believes that the views belong to a minority in the organisation who do not use the chaplaincy's services.
Mr Kevin Stanley, IDS chairman, said there had been some occasions when chaplains had involved themselves in ceremonies such as baptisms, funerals and weddings, without consulting deaf people.
In one instance, when a member's mother was being buried, the family organised the service with the parish priest. A chaplain arrived uninvited and prepared to concelebrate the ceremony. When the family told him that the parish priest was conducting the service, he left.
Mr Stanley said there had been other cases like this. "Chaplains should confine themselves to spiritual services for the deaf at the wishes of the deaf community, such as giving Mass and other religious services. At present, however, the chaplaincy appears in some cases to be acting far beyond its supposed remit of servicing pastoral care; it has become involved in issues of community and representation."
He said that the IDS tried to empower members of the deaf community to lead an independent life, whereas chaplains in other community or disability groups confined themselves to pastoral and spiritual services. He also criticised an arrangement whereby parish priests were encouraged to contact the Chaplaincy for the Deaf whenever a deaf person needed church services. This was an intrusion of their privacy, he said.
The IDS describes itself as the "foremost organisation of the deaf in Ireland, led by the deaf". It claims to have about 2,000 members, including the members of 25 local organisations.
The NADP has rejected the IDS criticism, saying that it had not received any complaints from the large numbers of deaf people who contacted the organisation every day. The association provides services and training for the deaf community and their families and has about 1,400 members.
Mr Niall Keane, NADP chief executive, said that the chaplaincy played a "very supportive role" in the deaf community.
"All service-providers, including ourselves, can be accused of being patronising at times," Mr Keane said. One person could see a service as supportive, while another could describe it as patronising.
