William Chapman died after entering the enclosure at the attraction in Doncaster on Sunday.
Yorkshire Ambulance Service Trust said it believed two staff had accessed or tried to access medical information “without a legitimate reason to do so” following the incident.
It said the concern had been identified “as a result of our proactive audits”.
The trust has started an investigation “to establish the full circumstances surrounding these potential breaches and the actions of these individuals”.
It said the Information Commissioner’s Office had been informed and William’s family will be kept up to date.
There have been other instances of NHS staff accessing medical information on high-profile cases without a legitimate reason.
The child attacked by a crocodile at a zoo in June had their records accessed by dozens of staff.
Southport attack survivor Leanne Lucas had her records inappropriately accessed and was not told until two years later.
The head of the NHS warned staff last month they faced immediate suspension if caught inappropriately accessing patient information.
Eleven staff were also sacked for accessing the records of the 2023 Nottingham attack victims.
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