I would hope there would be some kind of paper trail to import a crocodile into South Korea. Fortunately the crocodile was spotted before winter came which would have assuredly killed the reptile:

Police in Yeoju, Gyeonggi Province, have launched an investigation into how a critically endangered Siamese crocodile ended up in a local stream and who previously owned it.

Yeoju Police Station is reviewing surveillance camera footage from around Soyang Stream, where the reptile was captured Saturday, and interviewing nearby residents. Investigators are also checking whether anyone in the area previously registered a Siamese crocodile or a similar wild animal.

Korea Herald

You can read more at the link.