When the Chinese billionaire Ng Lap Seng was arrested in New York on bribery charges in 2015, a judge allowed him to await trial not in a jail cell but in a spacious apartment in Midtown Manhattan, with GPS monitoring and 24-hour armed security guards — all at Mr. Ng’s expense.

The case, in which prosecutors strongly opposed bail, is one of several in New York that have spurred debate over whether rich defendants are treated differently if they are able to persuade a judge that they will use their resources to ensure their appearance at future court hearings. In June, for example, another New York judge rejected such a request from a Turkish gold trader, saying the proposal helped to “foster inequity and unequal treatment in favor of a very small cohort” of extremely wealthy defendants.

In Mr. Ng’s case, a judge granted him a $50 million bond, secured by $20 million in cash and the apartment, at 240 East 47th Street. In recent months, Mr. Ng’s lawyers have continued to test the system, arguing that their 68-year-old client, who has pleaded not guilty and is scheduled for trial in May, should be allowed to go outside one day a week with his security guards, as they put it, “to walk in a park, to dine at a restaurant, to shop, to visit a museum, city landmarks, library or bookstores, or simply to be outside of his apartment.”

Prosecutors opposed the request. The office of Preet Bharara, the United States attorney in Manhattan, argued in court filings that Mr. Ng had immense wealth, access to private planes, multiple passports and no connection to the United States. Prosecutors called Mr. Ng an “extreme” risk of fleeing, and suggested that Mr. Ng, were he allowed more freedom, might slip away from his handlers and “dash into a car or disappear into a crowd.”