No open burning is allowed in New Haven: http://library.municode.com/HTML/14668/level3/TITIIICOGEOR_CH30.75WADI_ARTIINGE.html#TITIIICOGEOR_CH30.75WADI_ARTIINGE_S30.75-10OPBU
It appears curbside leaf collection is available in the fall: http://library.municode.com/HTML/14668/level3/TITIIICOGEOR_CH30.75WADI_ARTIINGE.html#TITIIICOGEOR_CH30.75WADI_ARTIINGE_S30.75-14MALECOPR
If you have the space, I would highly recommend composting the leaves or checking to see if you have a neighbor or nearby community garden with a compost bin that needs leaves. Leaves generally have a better nitrogen to phosphorus ratio than food waste and are an important component of any good compost system.
This was the answer that CAO Robert Smuts gave me when I asked, "You need a permit to burn leaves, and you go to the Fire Marshal's Office at 952 Grand Ave. We very, very rarely grant them, however, due to the scarcity of appropriate set-ups in our city where it would be safe."
Oops. Didn't see that this had just been answered by Brian Tang 13 minutes before me!
I've not been able to find this in the Municipal Code: http://library.municode.com/index.aspx?clientID=14668&stateID=7&statename=Connecticut
nor in the CT State Statutes: http://www.cga.ct.gov/asp/menu/statutes.asp
I'd suggest you call the Fire Chief: http://www.cityofnewhaven.com/Fire/index.asp [In most--if not all--towns leaf burning was banned long ago. Fire Pits seem to be less regulated, but I'd be surprised if they were legal in a densely populated area like New Haven.]
The ban is primarily motivated by environmental rather than safety concerns. Burning leaves produces particulate matter (soot), a form of air pollution. Even though I enjoy the smell, the pollution does exacerbate asthma and other health problems.