Hi danlow1. It ultimately depends on the church, but if your girlfriend is a baptized Catholic and has performed all her sacraments up to Confirmation, the Catholic church will marry you both permitting you attend pre-marital counseling sessions with the priest performing the ceremony and sacrament. Because marriage is one of the seven sacraments in the Catholic faith, it is advisable you contact the parish or cathedral where you wish to have your ceremony and ask to speak with the marriage coordinator to find out what exactly you'll need to do in order to wed there. Some may require she be a registered parishioner in their parish or have a document/letter from the presiding priest where she IS a parishioner. Others may not be so strict. Most require a certain percentage of your total wedding costs as a "donation" to the church in order to perform the ceremony. Some limit the use of flowers and dictate the kind of dress she can wear, others do not. Bottom line, while there are a few obstacles to marriage in a Catholic church, ultimately the fact that you are not a Catholic, or even baptized, does not preclude a Catholic church from marrying you if you meet whatever requirements that particular church has. This site has some good, basic information: http://www.aboutcatholics.com/beliefs/can-a-catholic-marry-a-non-catholic/ I hope this helps!
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