Why was no referendum held on the division of Czechoslovakia?

The decision to avoid a public referendum on the dissolution of Czechoslovakia was driven by the political leaders of the time, specifically Václav Klaus and Vladimir Mečiar.

Following the June 1992 elections, these leaders found themselves at an impasse regarding the future of the federation. Klaus, representing the Czech Republic, favored maintaining significant federal powers, while Mečiar, representing Slovakia, sought greater sovereignty. Because their political visions were fundamentally incompatible, they concluded that an operational federal government could not be formed.12

Although polls indicated that a majority of the population preferred to keep the country unified, neither Klaus nor Mečiar wished to submit the question of separation to a public vote. Consequently, the two leaders proceeded with negotiations to divide the state without seeking a popular mandate through a referendum. This process, known as the Velvet Divorce, culminated in the federal legislature voting to dissolve the country, which officially took effect on January 1, 1993.12