Health officials across New England are shuffling flu vaccine shots from hospitals and clinics with oversupplies to those facing shortages, raising questions about a flu shot distribution system that some critics say is inadequate.

It’s a patchwork system that some public health officials say is in need of reform, particularly in light of the potentially global threat from the spread of avian flu.

“We’ve seen proof that leaving something as essential as the flu vaccine supply in the hands almost entirely of market forces is grossly inadequate and certainly would lead to a great tragedy if we had a truly severe season,” said Dr. Dora Mills, Maine’s top health officer. “We need to have tracking down to the granular level.”

In Massachusetts, 7,000 to 10,000 doses of flu vaccine have been shipped back to that state’s Department of Public Health for redistribution to facilities facing short supplies.

Connecticut’s state health agency is helping clinics with too much vaccine send their supplies to centers facing shortages.

For example, a visiting nurse agency in Connecticut last week sent 950 flu shot doses to the Navajo Area Indian Health Service for distribution in New Mexico. The shots were shipped by overnight delivery service after Navajo health officials issued a nationwide plea for surplus vaccine.

Millions of flu shots tailored to predicted flu strains are distributed annually in the U.S. from October through January by government agencies and private companies.

The U.S. Centers for Disease Control and Prevention this month inaugurated a system that allows state health authorities to have access to a secure computer network with information about vaccine deliveries to a particular ZIP code.

Some officials say the system is not comprehensive enough because it doesn’t provide the names of doctors and clinics that received vaccines, or their precise locations.

Cooperation by private distributors is voluntary.

“The most frustrating thing to me is that FedEx can do that sort of detailed tracking of what it ships, but public health officials can’t do the same thing with flu vaccine,” said Dr. Georges Benjamin, executive director of the American Public Health Association. “The knowledge of where exactly vaccine is ought to be a public resource. We have a lot of work to do.”

Public health officials say the system gives them only a rough idea of how much vaccine is in their states. Rhode Island’s Department of Health is certain that 120,000 flu shots were shipped for children because the state bought that vaccine. But the agency can make only an educated guess in estimating there are 300,000 doses for adults.