The city should ease the path to college for top high school students by promising them free tuition at city colleges, Comptroller John Liu said [last week] in a “State of the City” speech, his second in 2012.

In the speech, Liu put forth a slate of policy proposals, including several focused on education, that he said would enhance the city’s economic future. Liu is a likely mayoral candidate, but as comptroller his job is to safeguard the city’s financial prospects.

“The offer of free tuition would help motivate students and elevate CUNY, one of our city’s most valuable gems, to the level of a competitive prize,” Liu said, according to his prepared remarks. “It would also be a life-saver for many working families who are struggling to send their kids to college.”

Liu did not explain how the city could fund the initiative, but it would not cost much. With tuition set at $5,400 a year, even if every student in the top 10 percent of each graduating class enrolled and would not ordinarily receive financial aid — an unlikely scenario — paying their way would cost less than $12 million a year.

Other proposals Liu made today would cost the city a lot more.

He proposed spending $75 million a year to provide home visits by nurses to thousands of needy families with young children, $32 million a year to give computers to students at high-poverty middle schools, and $176 million a year to add more guidance counselors to city high schools. Liu first proposed expanding the city’s fleet of guidance counselors in October, arguing that the expenditure would pay for itself with economic contributions from people who would not have gone to college without the counselors’ help.

And he said he would add social services to every city school, something the teachers union and city are jointly attempting in six schools this year, at a price tag of $100,000 a school. Liu said the proposal was inspired by a trip he took with City Council Speaker Christine Quinn to Cincinnati, which has embraced the “community schools” model that the union has been promoting.

“I’d like to see every New York City public school become a community center before and after school,” Liu said. “In addition to after-school programs, it could include a health clinic, and offer resources to parents and adults in the evenings, like tax advisory services and financial literacy courses.”

Most mayoral candidates were slow to respond to Liu’s proposals [last week]. But Tom Allon, whose candidacy as a Republican suffered a blow this week with the possible entrance to the race of former MTA Chairman Joseph Lhota, said he supported Liu’s call for a tuition break for top students and noted that it would require only a small expenditure. “Anything we can do to incentivize high school students to graduate and achieve high grades is a good public policy in my book,” Allon said.

The portion of Liu’s speech that focused on education is below: