I think this is referring to a Bahá'í marriage.

1. In New Mexico, "any ordained clergyman whatsoever, without regard to the sect to which he or she may belong may perform marriages".
http://www.usmarriagelaws.com/search/united_states/officiant...
In other words, the officiant can be a recognised leader of any spiritual denomination.

2. The word "Assembly" is specifically associated with the Bahá'í faith, which has National and Local Spiritual Assemblies.
http://en.wikipedia.org/wiki/Spiritual_Assembly

3. The Bahá'í faith is certainly practised in New Mexico; in fact it's historically quite strong there. Indeed, Mason Remey's "National Spiritual Assembly Under the Hereditary Guardianship" was incorporated precisely in New Mexico, in 1964.

4. There is a Bahá'í Local Spiritual Assembly in New Mexico, based in Albuquerque.

5. But how can an Assembly be a participant? The answer is that the Bahá'í faith has no clergy at all. No one officiates at a Bahá'í marriage; the "officiant" is the assembly itself.

"I believe you need two LSA members as witnesses. Then just follow the rest of the Bahá'í marriage requirements. No one "officiates" because we have no clergy, but you can ask someone to talk through the program as the MC so to speak"
http://bahaiforums.com/general-discussion/9288-bahai-marriag...

So if you have to record the officiant for a Bahá'í marriage, all you can put is the Local Spiritual Assembly.

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Note added at 1 hr (2014-03-28 12:22:30 GMT)
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Couple of corrections/additions to the above. On Mason Remey's Assembly in New Mexico, see
http://en.wikipedia.org/wiki/Bahá'í_divisions#Under_the_Here...

And under 5, I meant to write "how can an Assembly be an OFFICIANT".


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Note added at 1 hr (2014-03-28 12:37:44 GMT)
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And yes, there is a Bahá'í Local Spiritual Assembly in Santa Fe, which is where Santa Fe Bahá'ís would certainly marry. Here they are:
"The Local Spiritual Assembly of the Baha'is of Santa Fe"
"The Baha'i Faith has no clergy, and its affairs are administered by a network of elected lay councils at the international, national and local levels."
http://santafebahai.org/what-is-the-baha-i-faith.html

The US National Spiritual Assembly is in Evanston, Illinois, and there are no fewer than 1100 Local Spiritual Assemblies around the country.

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Note added at 1 hr (2014-03-28 12:45:39 GMT)
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"The LSA has the authority and the responsibility to oversee Baha'i weddings. In most places that I know about (which isn't the whole world, but it will have to do for now), the law requires that marriages be solemnized or otherwise overseen by someone legally empowered to do so, as opposed by anyone who happens to feel like doing it. Local Spiritual Assemblies generally have been granted that authority by the state. "
http://forums.delphiforums.com/n/main.asp?webtag=planetbahai...

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Note added at 1 hr (2014-03-28 12:48:35 GMT)
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That's great! Thanks for letting me know.