The Super Mario Bros. Super Show! episode Alligator Dundee
September 19, 1989
In the twelfth live action segment of the Mario TV show, broadcasted along with the cartoon episode "Stars In Their Eyes", the Mario Brothers meet a man called Alligator Dundee, who asks for their help to catch a monster he's going after. Later in the episode he shows them a picture of the monster, that they found to be the Ratigator, a rat-alligator hybrid introduced at the beginning of the episode a pet for them. After they manage to stop Dundee, he tells them that his dream was to become famous in New York for capturing the Ratigator and to fall in love with a beautiful american woman, something the brother find fitting for a movie plot, so Dundee finally decides to make a movie about this story, only changing his name to Ratigator Dundee.
It appears obvious that Alligator Dundee is based on the character Michael J. "Crocodile" Dundee, since both are australian crocodile hunters and wear almost exactly the same clothes, but another reference is in Alligator's story being a very short summary of the plot of "Crocodile" Dundee, and his plan to make it into a movie is a reference to it being an actual movie. Also note that at the end, after he decides to change his name, there's a short suspence pause, possibly to lead the audience into believing he was about to say "Crocodile Dundee".
It's unclear if in the show's continuity this is considered as an alternate origin to the movie, meaning that probaby in Mario's universe instead of "Crocodile" Dundee exists a movie called Ratigator Dundee or if "Crocodile" Dundee does exists as a movie in that universe, only Alligator Dundee isn't aware of it, because Mario and Luigi seem to recognise him at first, possibly meaning that they tought he was the character from the movie.
The Ratigator creature returns in some later episodes including "Mario Hillbillies".
The Super Mario Bros. Super Show! episode Crocodile Mario
November 28, 1989
The fiftieth episode of the Mario animated series (sixty-second also counting the Zelda episodes) is about the Mario Bros. the Princess and Toad traveling to an Australia-themed land called "Down Under Land" to get a Magic Statue that can protect Princess Toadstool's kingdom by scaring the crocodiles away, but as soon as they arrive it is stolen by Koopa's alter-ego Cangaroo Koopa, so Mario and Luigi go after him while the Princess, Toad and the local Toads are attacked by crocodiles. At the end the brothers manage to get the statue back and the Princess can use it to scare the Crocodiles, that then head toward Koopa, making him run away too.
This episode title, that's the nickname given to Mario, as well as Cangaroo Koopa, are references to Crocodile Dundee. The episode has a general australian theme, like the original movie, but its plot has no connection with Crocodile Dundee, apart from featuring Mario fighting a crocodile. However, the statue depicts an Australian hunter, likely based on Crocodile Dundee himself.
DiC, that created the Mario TV show, holds no right over Paramount Pictures' Crocodile Dundee, in fact they only parodied the movie, while never directly referencing it.