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A bill currently under consideration in the Connecticut General Assembly could provide the most dramatic change to state narcotics law in recent history.

Late last month, the legislative body’s Judiciary Committee approved a law to decriminalize possession of small amounts of marijuana, greatly reducing the penalty for possession of less than one ounce. While it lowers the disincentives for possessing marijuana, the bill will also decrease the burden on Connecticut’s criminal justice system and help ease the state’s budget crisis.

Currently, possession of one ounce of marijuana is a misdemeanor punishable by a fine of up to $1,000 and/or imprisonment for up to one year. But the GA’s bill reclassifies the offense as an infraction punishable by a $121 fine.

General Assembly staffers say there is a good chance the bill would garner a majority of votes. Several heavy-hitters in the legislature, including Senate Majority Leader Sen. Martin Looney and Sen. Toni Harp of New Haven, support the bill. But supporters of the bill say they do not have enough votes to override a presumed veto by Gov. M. Jodi Rell.

“The word in the Capitol is that it isn’t likely that the bill will be enacted this year, in part because Gov. Rell has threatened a veto and [the Democrats] don’t seem to have enough votes to override,” said one Democratic staffer with knowledge of the bill. “The leadership will have to make a decision whether they want to wage a fight on the floors of the House and Senate too.”

While Rell has expressed displeasure with the bill, she has yet to threaten to veto the legislation outright. In 2007, Rell vetoed a medical marijuana bill, saying at the time that she could not support legalizing the possession of a drug that would still be illegal to buy.

And indeed, the current proposal does nothing to change the fact that buying or distributing marijuana is illegal.

But even the current illegality has not deterred the nearly 10,000 yearly arrests in Connecticut for marijuana possession — approximately 33 percent of which are for possession of less than one ounce of marijuana.

Several students interviewed said that though buying and selling marijuana would still be punishable by imprisonment, they think the change in the law will cause more Yale students to use the drug.

“An ounce is a lot of marijuana,” said one student who did not wish to be identified. “Most students are not dealing drugs, and would be more likely to use marijuana now that they can’t be prosecuted for possessing less than an ounce.”

If this measure passes, Connecticut would be the 14th state in the nation to decriminalize the possession of small amounts of cannabis, said Allen St. Pierre, the executive director of the National Organization for the Reform of Marijuana Laws.

In a Quinnipiac Poll conducted last month, 58 percent of state residents expressed support for such a decriminalization measure.

But this bill would impact residents beyond just those who use marijuana, said Kica Matos, community services administrator for the City of New Haven. Matos said the cost of incarcerating offenders — $44,000 annually for adults and $100,000 annually for children — is reason enough for re-evaluation of the state’s drug policy.

“The proposed bill would not only reduce the [prison] re-entry population in Connecticut by decreasing the penalties for possession of small amounts of marijuana,” she said, “but in doing so would free up resources that are desperately needed to address substantively the real problems our cities face, from homelessness to re-entry, teen pregnancy to substance abuse.”

As it stands, the bill would cut state costs by as much as $11 million annually, according to the Office of Fiscal Analysis, while raising an estimated $320,000 in revenue for the state’s General Fund from fines on minor marijuana possession.

The bill was passed by the Judiciary Committee on March 31 and was referred Monday to the Office of Legislative Research and the Office of Fiscal Analysis, the next step on the road to law.

Harrison Korn contributed reporting.