If the construction is an emergency or "City of New Haven" related the activities are exempt from the Noise ordinance. Please feel free to call LCI about any quality of life issue at 203.946.7090.

Here is the applicable subsection of the ordinance:
http://library.municode.com/index.aspx?clientID=14668&stateID=7&statename=Connecticut

Sec. 18-78. - Exemptions and special conditions.

The following shall be exempt from these regulations, subject to special conditions as provided herein:

(1)

Noise generated by any construction equipment which is operated between the hours of 7:00 a.m. and 10:00 p.m. on Mondays through Saturdays, and 9:00 a.m. and 9:00 p.m. on Sundays. The building official or the director of the department of public works must approve the operation of the same during hours other than those allowed by this section. The person requesting such approval must apply for it at least seven (7) days before the date for which approval is sought. Approval may be granted if the requesting person makes an advanced payment for the actual cost of such inspection services as may be required under applicable rules and regulations as amended from time to time;

(2)

Noise created as a result of or relating to an emergency;

(3)

Noise from domestic power equipment such as, but not limited to, power saws, sanders, grinders, lawn and garden tools or similar devices operated between the hours of 7:00 a.m. and 10:00 p.m. on Mondays through Saturdays, and 9:00 a.m. and 9:00 p.m. on Sundays, provided that noise discharged from exhaust is reasonably muffled;

(4)

Noise from snow removal equipment, provided it is maintained in good repair and exhaust is reasonably muffled;

(5)

Noise from demolition work conducted between the hours of 7:00 a.m. and 10:00 p.m. on Mondays through Saturdays, and 9:00 a.m. and 9:00 p.m. on Sundays, provided that demolition shall be exempted at all times from the noise levels set in this regulation when it is considered emergency work;

(6)

Noise created by any aircraft flight operations, which the Federal Aviation Administration specifically preempts;

(7)

Noise created by any lawful recreational activities, and for which the city has granted a license or permit, including but not limited to parades, sporting events, outdoor concerts, firework displays and non-amplified religious activities;

(8)

Noise involving blasting other than that conducted in connection with construction or demolition activities, provided that the blasting is conducted between the hours of 7:00 a.m. and 10:00 p.m. on Mondays through Saturdays, and 9:00 a.m. and 9:00 p.m. on Sundays, at specified hours previously announced to the local public, or provided that a permit for such blasting has been obtained from local authorities;

(9)

Noise created by products undergoing tests, where one (1) of the primary purposes of the test is to evaluate product noise characteristics, and where practical noise control measures have been taken;

(10)

Noise generated by transmission facilities, distribution facilities and substations of public utilities providing electrical power, telephone, cable television or other similar services, and located on property which is not owned by the public utility, and which may or may not be within utility easements.

(Ord. No. 1422, 7-6-06)

I mean really whats the point of having rules if ya just special except them. What exactly is "City of New Haven" related activities ???

In other words you can call the number, but theres nothing LCI can do about any quality of life issues.