Eddie:
IIRC, Texas does not have any "private sale" (citizen to citizen or individual to individual) registration requirements or NCIC checks, etc. I
would write up a "Bill of Purchase/Sale" for you both to sign, however. I'll take a quick peak elsewhere and let you know........
See:
SECONDARY SALES
Are background checks required on 'private' gun sales? No
No state requirement that criminal background checks be done on people buying firearms at gun shows, swap meets or through newspaper or internet advertisements. Criminal background checks are only required if the buyer goes to a federally-licensed gun store - all other sales are not subject to the background check.
Also:
LICENSE OR PERMIT TO PURCHASE
Is a license/permit required to buy handguns? No
No state requirement that handgun buyers obtain a handgun license or undergo any type of safety training prior to buying a handgun.
And:
GUN SHOW CHECKS
Are background checks required at gun shows? No
No state requirement that a Brady criminal background check be done on people buying guns at gun shows if they are sold by "private" individuals or gun "collectors." Gun shows can operate on a "no questions asked, cash-and-carry" basis, making it easy for criminals and even juveniles to buy as many guns as they want at gun shows, including assault weapons. No records are required to be kept on gun show sales by private individuals or gun collectors, making it almost impossible for police to trace such weapons if they are used in a crime.
As well as:
REGISTRATION
Are all guns registered with law enforcement? No
No state requirement that gun owners register their firearms. Police do not know how many guns are in the state or where they are. The lack of registration data makes it more difficult for police to trace guns used in crime, identify illegal gun traffickers or hold gun owners accountable for their weapons. There is no state system to automatically identify and disarm felons and other prohibited people who bought guns legally in the past, but later committed a crime or otherwise became ineligible to keep possession of their firearms.
Excerpts from:
http://www.stategunlaws.org/viewstate.php?st=TX