An additional candidate may soon turn the four-way contest to replace Mayor John DeStefano Jr. into a five-man race — that is, as long as Hillhouse High School Principal Kermit Carolina can find sufficient community support for his campaign.

After signaling he might be interested in the job in January, Carolina officially revealed he was considering a run for mayor in a Tuesday press release. The statement announced the formation of an exploratory committee designed to gauge the viability of Carolina’s candidacy. Committee member Bob Pellegrino said that in the coming three weeks,  he will reach out to city residents to share details about Carolina’s commitment to the city and to determine initial support.

“If I had to guess, I would say he’s going to make the run,” Pellegrino said. “He’s well situated to do so at this point.”

Jack Paulishen, a civics teacher at Hillhouse High School who co-chairs the 18-member exploratory committee, said that if initial response is any indication, he thinks his candidate will “seriously consider running.”

Should he choose to run, Carolina will enter a field that currently includes Ward 10 Alderman Justin Elicker FES ’10 SOM ’10, Connecticut State Rep. Gary Holder-Winfield, Fernandez Advisors CEO and former New Haven Economic Development Administrator Henry Fernandez LAW ’94 and Sundiata Keitazulu, a plumber in New Haven. A final candidate, Probate Judge Jack Keyes, has all but indicated he will join the fray.

What sets Carolina ahead of the pack, Pellegrino and Paulishen said, are his deep ties to New Haven.

“Kermit was born and raised in this city,” Pellegrino said. “He’s lived here his whole life and he’s educating his sons in this city. You can’t say the same thing for the other candidates.”

Pellegrino added that Carolina has access to a “bird’s eye view of education” as a high school principal. He said this would help him cut costs in areas that other candidates might not know about.

Before becoming principal in 2011, Carolina was the high school’s basketball coach, a position he held for nearly a decade after working for a number of years in the school district. Carolina grew up in the Ashmun Street Housing Projects before attending Southern Connecticut State University.

“As a lifelong resident of the city of New Haven, my strong connection and love for this city have served as the basis for many years of my public service here,” Carolina said in his press release.

His work in the city has not been without conflict, though, as Carolina sparred publicly with DeStefano and Public Schools Superintendent Reginald Mayo last fall over reports of grade tampering for student athletes at Hillhouse. The Board of Education ended up issuing Carolina a three-day suspension-without-pay order, a move that the principal is still fighting in arbitration, Pellegrino said.

Paulishen said the conflict is evidence that his candidate is not afraid of standing up to “the powers that be.”

That’s also the message Pellegrino conveyed in describing Carolina’s commitment to public campaign financing under the New Haven Democracy Fund, a system that limits private donations in return for a public grant and matching funds. So far, all candidates have said they will use the Fund except for Fernandez. In his statement, Carolina went as far as to commit, under “the spirit of the Democracy Fund,” not to begin fundraising while still in the exploratory phase.

Pellegrino said this move would help separate Carolina from the “machine” that he said often dictates elections in New Haven.

“There are other forces getting people elected here, whether it’s unions or the sort of political cronyism we saw under DeStefano for the past 20 years,” Pellegrino said. “I don’t know what Fernandez’s motives are for not using public money but my suspicion is that he wants the ability to get high-heeled donors. Fernandez worked under DeStefano as the economic development administrator, so he would be the most natural candidate to represent the machine. That’s how it works when you get big campaign donations and favors from people and then give them contracts in return.”

Fernandez has declined to comment on what he called “procedural” questions of campaign finance, saying only that he has a “very strong track record on the issues — on reducing crime, improving our schools, creating youth centers and creating jobs.” He also declined to comment specifically on Carolina’s formation of a committee to explore running for mayor.

In response to the announcement, Elicker said only that he thinks highly of Carolina and looks forward to hearing more about his ideas. Holder-Winfield could not be reached for comment Tuesday afternoon.

The Democratic Primary will be held on Sept. 10.