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The decision by Richard M. Platkin, an acting justice on the State Supreme Court, came less than three weeks before Election Day. The ballot question would amend the State Constitution to allow up to seven casinos.

Eric J. Snyder, a bankruptcy lawyer living in Brooklyn, had objected to the positive descriptive language in the measure’s ballot abstract, which describes the referendum as “promoting job growth, increasing aid to schools and permitting local governments to lower property taxes.” The language was approved by the State Board of Elections in late July after consultation with the administration of Gov. Andrew M. Cuomo, who supports the measure.

In filing his suit, Mr. Snyder, who opposes casinos, said that the language had unfairly tilted the measure toward passage, something borne out by a recent Siena College poll showing that support for it increased by nine percentage points when the respondents were read the ballot abstract citing jobs, aid to schools and lower taxes that could result from opening the casinos.

After the judge’s decision, Mr. Snyder said he would seek emergency relief from the appellate courts, noting that the board had disregarded a simpler version of the referendum — without what he called “advocacy language” — that had initially been suggested by the office of the state attorney general, Eric T. Schneiderman.

“Ignoring the attorney general’s recommendation, the Board of Elections changed the neutrally worded casino amendment by adding language to gain voter support,” Mr. Snyder said in an e-mail, adding that “transparency and proper notice are fundamental rights in this country, and that includes New York.”

In dismissing the case, though, Justice Platkin said Mr. Snyder’s suit, filed on Oct. 1, had come after the statute of limitations for such ballot-language challenges had passed. (Such challenges are limited to a 14-day window after a referendum’s final day to be certified; this year, that deadline was Aug. 19.)

And while Mr. Snyder had argued that he was not aware of the language at that point, and that the Board of Elections did not post the referendum to its Web site until Aug. 23, Justice Platkin seemed unimpressed. “The petition/complaint would still be untimely,” he wrote in his decision.

Thomas E. Connolly, a Board of Elections spokesman, said, “We’re pleased that Judge Platkin accepted the legal arguments which we raised and that the election process can continue moving forward.”

But government watchdog groups that had criticized the ballot language were unhappy. One of the organizations, the New York Public Interest Research Group, said in a statement, “We’re disappointed that the judge chose to block a legitimate discussion on the merits of whether the state gamed the language of the casino amendment to tilt New Yorkers to a yes vote.”