We cannot know for certain, but I would estimate that the odds are greatly in your favor regarding the actual date of naturalization; Tarquinio was still Italian in late January, 1920 and Mario was born that same year?
Your best bet is to go ahead and locate copies of Tarquinio's naturalization documents. There are two primary sources which you can try:
First, The US National Archives For general info:
http://www.archives.gov/genealogy/natur ... ation.html
To order records, go to
https://eservices.archives.gov/orderonl ... chives.gov
Click "Order Reproductions", then "Immigration and Naturalization Records". On the next page, click "Naturalization Records" and on the next page, use the dropdown "Select a Delivery Format" to select "Certified Paper Copy" (you'll eventually need a certified copy for your citizenship petition, but you can begin with a non-certified copy for research purposes if you prefer).
The National Archives response time is generally very fast (as little as a few weeks) and not terribly expensive. On the other hand, in many areas including New York, the National Archivies holds records only for naturalizations which took place in the federal court system. At the time in question, a majority of naturalizations actually took place in state and county courts.
The other major option is to go directly to the US Citiznehsip and Immigration Service - USCIS. It will cost more and take longer (months).
Go to
http://www.uscis.gov/portal/site/uscis/ ... 18190aRCRD and click "Make a Genealogy Request" on the right side of the page. You will need to do an "Index Search" first in an attempt to locate records and , presuming that comes back successfully, you then follow up with a "Records Request".
I hope you will keep in touch and let us know how this turns out!
