South Carolina regulators on Tuesday rejected an effort by the Trump Organization to limit its environmental cleanup liabilities at an industrial site once owned by President Trump’s eldest son.

The decision is a rebuke of the Trump Organization and could result in millions of dollars in added costs for the company. It followed a refusal by the organization to provide regulators with required information about business and financial relationships between the president and his son Donald Trump Jr.

The Trump Organization had no immediate comment.

The issue grew out of the younger Mr. Trump’s involvement in Titan Atlas Manufacturing, a company that he helped start in 2010 in North Charleston, S.C., and that failed two years later.

In 2014, Donald J. Trump, while he was still running the Trump Organization, bailed out his son, who was then facing payment of a $3.65 million bank loan to Titan Atlas. The elder Mr. Trump created an entity called D B Pace, which took over the loan and the six-acre Titan Atlas site.

Last year, D B Pace applied to take part in a state program that would limit the company’s liabilities for pollution on the property, like chemical contamination of groundwater.

To qualify for such protection, however, the buyer of a contaminated property must not be affiliated with a former owner or have had earlier involvement with the site. The safeguard is in place to prevent polluters from evading their legal responsibilities.

A Trump Organization lawyer, Michael Cohen, stated in D B Pace’s application that it met that standard because it had no ties to Titan Atlas and had never been involved in the management of the North Charleston property.

But in December, an article in The New York Times reported that filings in a lawsuit by a former tenant showed that Donald Trump Jr. and Mr. Cohen had managed the Titan Atlas property for two years before D B Pace applied to the state’s program. Last month, the South Carolina Health and Environmental Control Department sent a letter to Mr. Cohen, demanding information about all familial, corporate and financial relationships between the principals of D B Pace and Titan Atlas.

In the letter Tuesday to the Trump Organization affiliate, South Carolina officials said that D B Pace had decided not to provide the required information. For that reason, the agency said, it would not allow the company to participate in the program, known as the “brownfield” cleanup program.

Had the application gone through, the Trump Organization’s costs would have probably been minimal because its environmental obligations would have been limited to controlling the spread of existing pollution on the property. But now, it is likely to be legally responsible for pollution at the site caused by Titan Atlas.

The decision by the Trump Organization appears to reflect a financial gamble that any environmental costs from the Titan Atlas site might be less than the financial damages it could face by disclosing ties between D B Pace and Titan Atlas.

D B Pace has taken the position in a $4.5 million lawsuit brought by a former tenant at the Titan Atlas warehouse that Donald Trump Jr. had nothing to do with the building’s management. However, court papers show that the younger Mr. Trump and Mr. Cohen, the lawyer, repeatedly rejected requests from the tenant to fix the building’s leaky roof unless the tenant extended its lease.

The roof failed in late 2015 after days of rain, and the tenant, Saint-Gobain Adfors, has claimed it lost $4.5 million in stored products.