Catholic Apostolic Church Records in the United States

History
The Catholic Apostolic Church was a religious movement which originated in England around 1831 and later spread to Germany and the United States.While often referred to as Irvingism or the Irvingian movement, it was neither founded nor anticipated by Edward Irving. The church was organized in 1835 under the lead of self-proclaimed apostles. Source: Wikipedia

Correspond with or visit the actual churches.
Records are still held in the local churches. Contact the current minister to find out what records are still available.
 * Make an appointment to look at the records. Or ask the minister of the church to make a copy of the record for you.
 * To find church staff available, you might have to visit on Sunday.
 * Ask for small searches at a time, such as one birth record or a specific marriage. Never ask for "everything on a family or surname".
 * A donation ($25-$40) for their time and effort to help you would be appropriate.
 * If the church has a website, you may be able to e-mail a message.
 * See the Letter Writing Guide for Genealogy for help with composing letters.
 * Catholic Apostolic Parishes and Missions

Carefully compare any record you find to known facts about the ancestor
You will possibly find many different people with the same name as your ancestor, especially when a family stayed in a locality for several generations, and several children were named after the grandparents or aunts and uncles. Be prepared to find the correct church records by gathering in advance as many of these exact details about the ancestor as possible:
 * name, including middle name and maiden name
 * names of all spouses, including middle and maiden name
 * exact or closely estimated dates of birth, marriage, and death
 * names and approximate birthdates of children
 * all known places of residence
 * occupations
 * military service details

Carefully evaluate the church records you find to make sure you have really found records for your ancestor and not just a "near match". If one or more of the details do not line up, be careful about accepting the entry as your ancestor. There are guiding principles for deciding how to resolve discrepancies between records that are seemingly close. For more instruction in evaluating evidence, read the Wiki article, Evaluate the Evidence.