Stabile, whose family said he was an avid outdoorsman who loved to surf, had been at the park on vacation.
Fabrizio Stabile came down with a "severe headache" while mowing his lawn in Ventnor, NJ., on September 16.
Parsons said the park has voluntarily closed pending the results of the CDC testing.
The amoeba, called Naegleria fowleri, is typically seen in fresh water.
Though it's unclear exactly how the man, 29-year-old Fabrizio Stabile, got the amoeba, the Centers for Disease Control and Prevention (CDC) is now investigating BSR Cable Park's Surf Resort in Waco, Texas, the Waco Tribune-Herald reported on September 28. The amoeba is commonly found in warm freshwater such as lakes, rivers, ponds and canals.
It usually infects people when contaminated water enters the body through the nose.
The Centers for Disease Control announced Friday that it is testing the waters at BSR Cable Park Surf Resort, in Waco, Tx., amid fears Stabile contracted the illness there. He later died of primary amoebic meningoencephalitis caused by the amoeba.
He died five days later and tested positive for Naegleria fowleri the day before his death, his family said.
"BSR Surf Resort operates a state of the art artificial man-made wave", he said.
It causes the nervous-system infection primary amebic meningoencephalitis (PAM) by traveling up a person's nostrils and into their brain, but can not be transmitted if a person swallows water contaminated with the bug.
Parsons said his resort's wave pool is in compliance with the CDC's "guidelines and recommendations concerning Naegleria fowleri".
A GoFundMe page has been set up as The Fabrizio Stabile Foundation, where more than US$22,000 of a $50,000 target has been raised so far.
Of the 34 cases reported in the U.S. between 2008 and 2017, 30 people had been infected by recreational water, three people were infected after performing nasal irrigation using contaminated tap water, and one person was infected by contaminated tap water used on a backyard water toy.