I would recommend doing so, because it makes for a richer viewing experience (the music even references the earlier film towards the end, in a euphoric moment for Ghibli fans), but it’s far from necessary. It’s not actually stated in the film, so you don’t need to have seen Whisper of the Heart first.
The real Muta inspires the fictional Muta in The Cat Returns. That’s also why Muta appears in both films. The idea here, and it’s a rewarding one for fans of the film series, is that Shizuku from Whisper of the Heart managed to polish the gem inside her and write her story, inspired by the Baron statue. “The Cat Returns” is obviously a reference instead to the Baron, who appeared as a statue and in a dream sequence in Whisper of the Heart. But the original Japanese title translates better as “The Cat’s Repayment”, referring to the actual plot of the film (Haru’s reward for saving the prince). “The Cat Returns”: that really sounds like a sequel, doesn’t it. The first thing to recognise here is that the title is misleading, and that only happens for the English translation. There is one slight exception to that, and it’s hardly a sequel at all, but The Cat Returns is strongly connected to Whisper of the Heart. But the Studio seems to have an admirable approach of always looking forward and doing something fresh and different. Several other films are ripe for a sequel, My Neighbour Totoro in particular.
Spirited Away won an Oscar, but never got a sequel.
Studio Ghibli don’t really go in for sequels.