How can i find out if my great grandmother was naturalized by being married to my great grandfather when he naturalized. Or if she did it on her own. GENOEFFA SACCOMANDO A2364555. She was born in Sicily in 1900 and came over through NY 11/4/1914.

Here's an essay about "Women and Naturalization" that should answer whether she would have derivative citizenship.  https://www.archives.gov/publications/prologue/1998/summer/women-and-naturalization-1.html

When did they get married?  Was your great grandfather born in the U.S.?  If not, when or if did he become naturalized?  Do you have his naturalization documents?  If you want the research committee to help, her name, birth place and date, etc. would be helpful.  Otherwise you will get generic responses.

I'm having no luck finding my great grandfather's record. Ignazio Saccomando.  Birthplace Sommatino italy Aug 10,1891. Genoeffa Saccomando birthplace Santo Stefano DiCam-mastra, Sicily feb 8, 1901 +/- a year. They were married in italy and came over through NY 11/4/1914

She was born Santo Stefano DiCam-mastra, Sicily feb 9 1900. Ignazio Saccomando born. Aug 10 1891. Married in italy. Don't have his naturalization records. 

#1
I doubt that Ignazio and Geneoffa were married in Italy because Genoeffa is still single when she arrives and will be joining her brother in New York.
Her 1914 arrival: https://www.familysearch.org/ark:/61903/3:1:3Q9M-C9TX-W96L-1?i=1014 (#8).

#2
In the 1930 census Ignazio is NAturalized, while Genoeffa is still an ALien. By 1940 both are NAturalized => So no, Geneoffa did not naturalize automatically with her husband.

And Finally #3:
Here is “Genueffa’s” birth cert: https://www.familysearch.org/ark:/61903/3:1:3QS7-89CY-CCVP?i=20 (#28)
DOB is 8 FEB 1899 in Santo Stefano di Camastra, Messina, Italy …

Thank you so much. Do you have a link to the 1930 census?

As Frank and Jennie:

1920 Census: https://www.familysearch.org/ark:/61903/3:1:33S7-9RXS-79C?i=5 (#65)

1930 Census: https://www.familysearch.org/ark:/61903/3:1:33SQ-GR8H-18F?i=18 (#5)

1940 Census: https://www.familysearch.org/ark:/61903/3:1:3QS7-89MT-57F5?i=9 (#42)

As Ignazio and Genevieve:

1950 Census: https://www.familysearch.org/ark:/61903/3:1:3QHN-GQHW-FGG8?i=11 (#19)

Thank you I was able to locate her naturalization records. I requested them from the USCIS I assume they send me a certified copy for 65.00. I gave them he c file number.  

I do have a question about ordering a birth certificate from Italy. I see you found her on familysearch. But when I go to the italian portal in Messina. I cannot seem to get her to populate from a search. Any suggestions. You have been amazing and so helpful.