Boston Public Schools officials fended off an attempted state takeover and now are looking ahead to a new superintendent in Dorchester’s own Mary Skipper. But Skipper and other top school officials will be facing a drop in satisfaction from parents of K-12 students in the system, according to a new survey from MassINC Polling Group.

In the poll, conducted for the Shah Family Foundation, only 29 percent of public school parents said they were “very satisfied” with Boston’s schools, a drop from 41 percent a year ago.

Some 43 percent said they were “somewhat” satisfied while 15 percent and 11 percent said they were “somewhat” dissatisfied and “very” dissatisfied.

Latino and Asian parents, who are more likely to believe Boston school officials are focused on serving students rather than teachers and politicians, and parents with an education level of high school or lower indicated higher satisfaction rates.

When asked about how well Boston Public Schools communicates with parents, a majority said they feel their input is “somewhat” valued, but half or less said they “strongly agree.”

Parents were also quizzed on where $430 million in Covid relief funding should go. They answered mental health needs, building upgrades, instructional materials, and staffing.

Most parents say they are closely following news about the school system, with forty percent saying they would choose a Boston public school even if they had other options.

“Parents want to be more engaged with their children’s education, with 83 percent saying they want to be ‘very engaged.’ Even so, just 45 percent feel that BPS enables them to be ‘very engaged,’” the polling outfit said in a statement. “On a similar note, 37 percent strongly agree that BPS makes it easy for them to share their concerns and 30 percent strongly agree their feedback is valued. Each of these figures has declined over the last year.”

Skipper, who is leaving the top job in the Somerville public school system and formally starting in Boston on Sept. 26, won the superintendent’s post in a close Boston School Committee vote in June. The runner-up was Tommy Welch, the regional superintendent for schools in Charlestown, East Boston, and the North End.

As Skipper transitions between school systems, Drew Echelson is serving as acting superintendent.

Skipper, who worked in Boston for 17 years before heading to Somerville in 2015, is tasked with working with school leaders and Mayor Michelle Wu, a mother of two boys in the Boston public schools. The new superintendent notably headed up Dorchester’s TechBoston Academy, where students focus on science and engineering.

During the interview process for Boston superintendent, Skipper said that building trust with parents, with a healthy dose of honesty, is key. “I heard many parents talk about feeling that they can’t trust what happens and that even if it’s not the right answer, they just want the truth,” she said at the time.

The sponsor of the MassINC poll, The Shah Family Foundation, is headed up by Jill Shah, an entrepreneur, a mother and the wife of Niraj Shah, CEO of the e-commerce company Wayfair.