Mayor Thomas M. Menino today asked the Patrick administration for $15 million to handle a potential influx to the city of hundreds of inmates whose convictions may be undone by alleged evidence tampering at a state drug testing laboratory.

Menino wrote that the city believes the state has a duty to help cover the costs that are expected to grow out of the scandal centering on former state chemist Annie Dookhan, whom officials fear may have tainted 60,000 drug samples involving 34,000 cases.

In his letter to Administration and Finance Secretary Jay Gonzalez, Menino said Boston anticipates that some 600 people will be returning to the community earlier than expected, and that the city is concerned about the impact they will have on the crime rate, rental housing, demand for emergency shelter, and the cost of job training and mental health counseling, among other issues.

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“We intend to request the Commonwealth's assistance in meeting those needs,’’ Menino wrote.

City officials last week said they would put more police on the street to deter criminal activity and create “crisis reentry teams” of police, probation officers, and outreach workers to oversee the freed inmates.

Many of the inmates who may be freed in the coming days have long histories of violence and drug trafficking, police and prosecutors say. Officials are meeting today with sentenced inmates who may soon have their sentences stayed, have their convictions overturned completely, or be freed on much lower bail amounts than initially imposed.

Menino said the effort is “intended to mitigate the impact in our neighborhood of approximately 600 individuals re-entering society from state institutions. ... I know that we share a common purpose in protecting our neighborhoods and in making sure that we don’t backslide from recent gains in violence prevention, neighborhood stability, and opportunity creation,” Menino wrote.

The city’s request is the second of what is expected to be a slew of multimillion-dollar pleas for state assistance from the Committee for Public Counsel Services, the Trial Courts, and law enforcement agencies like State Police and the Department of Correction.

The Globe has reported that prosecutors, through the Massachusetts District Attorneys Association, are planning to seek at least $10 million a year for the next several years to pay for more prosecutors, support staff, and equipment needed to update current cases and resurrect closed cases dating back to 2003 when Dookhan joined the Jamaica Plain lab.

The administration has asked that the budget requests be filed with them by Oct. 24.

Also today, Suffolk Superior Court Judge Christine McEvoy is presiding over the first special session created solely to hear Dookhan-related cases for Suffolk County, composed of Boston, Chelsea, Winthrop and Revere.

According to Suffolk District Attorney Daniel F. Conley’s office, about 23,000 drug samples of the total feared mishandled by Dookhan are tied to Suffolk County prosecutions.

More than 20 people, most of whom are currently incarcerated in the state maximum security prison in Walpole, are asking to at least have their state prison sentences put on hold — or “stayed” in legal terms — while the state investigation into Dookhan’s alleged misdeeds continue. Some are hoping that McEvoy will toss out their convictions outright in those instances where there is information that Dookhan directly handled the drug testing in their cases.

Since mid-September, similar hearings have been held, usually on a much smaller scale in terms of the number of defendants involved, in courthouses across eastern Massachusetts. More than 20 men and women have been completely freed, or have been released once their sentences have been stayed, since then.