SINGAPORE—Fourteen years ago, a Hello Kitty sales promotion here spiraled out of control, threatening to disrupt the peace in this order-obsessed Asian city-state. Historians called what happened a "fever," while lawmakers debated what should be done to end the plushy pussy mayhem.

Now a new set of the famous Japanese cartoon characters are coming—and Singapore's ability to play nice with its Hello Kitty toys is about to be put to the test.

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