Attorney General Maura Healey leads the Democratic race for governor with 48% support from likely voters seven months from primary election day, according to the first major poll conducted since she entered the race to succeed Gov. Charlie Baker.

Boston Sen. Sonia Chang-Díaz placed second with 12% and Harvard professor Danielle Allen was third with 3% among Democratic primary voters. Four percent preferred another candidate, 4% said they would not vote. A large percentage of those surveyed, 30%, refused the question or had no preference, indicating that a significant number of Democrats are undecided.

"Particularly in party primaries, voters often take a much longer time to make up their mind. One of the big reasons for that is there are more candidates who are within their kind of ideological space," said Steve Koczela, president of MassINC Polling Group, which conducted the poll.

In the Democratic race to replace Healey as attorney general, former Boston City Councilor Andrea Campbell, who has not yet declared but is expected to announce soon, was the clear leader with 31% support. Attorney and activist Shannon Liss-Reardon placed second with 3% and Quentin Palfrey with 2%. Fifty-four percent of respondents were undecided.

The poll also found that 45% of overall respondents want a governor "about the same as Charlie Baker." When limited to likely Democratic primary voters, 51%, said they want the next governor to be on par with Baker's moderation, with 38% saying they'd want a more liberal chief executive.

"A majority of Democratic primary voters do not want the next governor to be more liberal than Charlie Baker. At least that's what they're saying right now," Koczela said.

A separate poll question asked about the Democratic primary race if it included Labor Secretary and former Boston Mayor Marty Walsh, with Walsh narrowly beating out Healey 32% to 31%. Walsh said on CNN in January that he would not run for governor of Massachusetts.

Methuen Sen. Diana DiZoglio has a narrow 13% to 12% lead over former Assistant Transportation Secretary Chris Dempsey in the Democratic race to succeed Suzanne Bump as state auditor, though 64% say they're undecided.

The highly contested field for lieutenant governor also showed 64% of respondents were unsure of who to support, but Salem Mayor Kim Driscoll had twice as much support, with 10%, over Rep. Tami Gouveia, Sen. Adam Hinds and Sen. Eric Lesser, who all polled at 5%.

The poll did not ask about the race between incumbent Secretary of State William Galvin and NAACP Boston president Tanisha Sullivan, since the poll was in the field prior to their campaigns launching.