The film is actually based around the premise that it is a story created by Shizuku Tsukishima, the protagonist of 'Whisper of the Heart.' If one watches both films, they may find the following connections:
1)The Baron- In 'Whisper,' he was a statue that Shizuku found when she visited the antique shop of Seiji Amasawa's grandfather. The Baron also became the subject of a story she chose to write, titled 'If You Listen Closely.' It is not known if 'The Cat Returns' is a continuation of this work.
2)Muta- In 'Whisper,' Shizuku encountered a large cat on a train ride to the library. After getting off the train, she followed the cat, which eventually led her to the Amasawa's antique shop. Later on, Seiji Amasawa tells Shizuku that the cat is known by many names, including Moon (because he 'looks like a full moon') and Ball. On a late night outing Shizuku encounters the large cat again, and hears a little girl call him Muta. In 'The Cat Returns,' the large cat is referred to by Baron as Muta. In the Cat Kingdom, a legend knows him by the name of Renaldo 'Moon,' a gluttonous cat who ate all the fish in the kingdom's lake. There is also a sense of connection between Shizuku's experience and that of Haru, in that a large cat led them to a strange and magical place where they encountered The Cat Baron (for Shizuku it was the Amasawa's antique shop, for Haru it was The Cat Bureau).
Sunset- This was a key moment in 'Whisper,' where Seiji showed how sunlight reflected in the Cat Baron statue's eyes created an interesting effect. This moment is somewhat repeated in 'The Cat Returns,' when Haru finds The Cat Bureau at sunset, and the sunlight shines in his eyes at the Bureau's front window.
However, it is also possible that this film is in fact a sequel. As the Baron states in reference to Toto, "When a person creates something with all of their heart, that creation is given a soul." It is possible that the Baron is the soul of the cat statue seen in 'Whisper of the Heart'. Muta could also be the cat that Shizuku followed to the Amasawa's antique shop, though the change in his appearance would suggest that this happened years ago. If this were the case, then the antique shop would most likely be where Muta have met the Baron.