12 CFR § 1240.62, promulgated by the FDA, prohibits the sale of turtles that are less than 4 inches in length. However, there are some exceptions and a number of businesses have tried to find loopholes to exploit the exceptions. See https://www.thespruce.com/illegal-sale-of-turtle-hatchlings-in-united-states-1239414. The FDA asks that anyone who has knowledge of sales or distribution of turtles less than 4 inches in length report the location and circumstances of the sales directly to the FDA office nearest their location. This link: http://www.countyoffice.org/ny-fda/ provides the NYS FDA offices by county.
In view of this, the veterinarian can certainly treat the turtle. And the veterinarian does not have an obligation to report to the FDA but can if that’s the way they’d like to proceed. The veterinarian should bear in mind that the owner might not be too happy if a report is made to the FDA. This is especially true because we do not know how the owner acquired the turtle and the regulation does not apply to the mere possession of a turtle.