Gov. Larry Hogan (R) speaks during a news conference in March as Lt. Gov. Boyd Rutherford, left, listens. (Brian Witte/AP)

Maryland Gov. Larry Hogan vetoed a bill Friday that would create a new method for deciding which transportation projects are funded, setting the stage for a veto-override battle with the Democratic-controlled General Assembly in the final days of the three-month legislative session.

The measure was one of several bills presented to Hogan (R) on Friday as part of an effort to force the governor to decide on vetoes in time for Democratic lawmakers to override them before the legislature adjourns April 11.

In a letter to the legislature explaining his veto, Hogan called the transportation bill “the worst kind of policymaking” and said it establishes “arbitrary new criteria to guide transportation decisions in Maryland.”

He also said the bill — which would require the state to rate transportation plans before deciding which projects to fund — “miserably fails” his “simple test” on whether a law or action makes it easier for families and small businesses to stay in the state and whether it helps attract new families and businesses.

House Speaker Michael E. Busch (D-Anne Arundel) said the bill provides transparency. “People ought to understand where their $12 billion worth of taxes are being spent for road projects and mass transit,” he said. “It doesn’t limit the governor in any way; it doesn’t tie his hands. But it does disclose to the public where the greater needs are, where the economic impact is and what the safety implications are.”

Overturning a veto requires the approval of three-fifths of both the 141-member House of Delegates and the 47-member Senate. Neither chamber passed the bill with a veto-proof majority, but several Democratic lawmakers were absent the day of the vote.

There are 91 Democrats in the House, six more than are needed for an override, and 33 Democrats in the Senate, four more than needed.

In addition to the transportation bill, the General Assembly presented Hogan with the capital budget, over which he has line-item veto power; a bill that provides aid to Baltimore, including education and demolition programs; and a measure that strips Hogan of his five appointments to the Anne Arundel County school board. He has six days to decide whether to veto them.

Some of the other bills already presented to Hogan are not controversial. They include a measure that raises the maximum age that surviving children of police officers killed in the line of duty can receive benefits from 18 to 26 years old. The bill will apply retroactively to the children of two Harford County sheriff’s deputies who were killed in February.

Also on Friday, the Senate voted 34 to 11 for a bill that would prohibit universities from reporting certain delinquent student accounts to collection bureaus.

The bill would allow certain part-time students to register for classes even if they have a small unpaid balance on their accounts. The measure now heads to the House for consideration.

In the House, lawmakers gave preliminary approval to a criminal justice bill designed to reduce the prison costs and population while alleviating sentencing disparities that have disproportionately affected African American men.

Lawmakers debated an amendment that would stiffen the penalty for child abuse that results in death, lifting the current maximum sentence of 40 years and allowing judges to sentence offenders to life in prison. The amendment passed 72 to 59.

Del. Kathleen M. Dumais (D-Montgomery), who opposed the provision, said that the change would run counter to the goals of the legislation and that the state needs a “shift in the paradigm.” Del. C.T. Wilson (D-Charles), who requested the amendment, agreed that Maryland needs to change how it deals with nonviolent criminals but said the state also needs to have a “shift in the way we treat our most violent offenders.”

The House’s criminal justice measure is vastly different from the Senate version of the bill. Delegates added amendments that would eliminate mandatory minimum sentences for nonviolent drug offenders and increase penalties for leaders of gangs and organized crime. Those differences must be reconciled in a conference committee in order for the bill to go to Hogan’s desk.

The House on Friday also gave preliminary approval to a bill that would require businesses with 15 or more employees to provide an hour of paid sick leave for every 30 hours worked. Lawmakers in the chamber rejected an amendment that would exempt restaurants. Existing language in the legislation exempts agricultural employees.

Republicans raised concerns that the measure would create a burden for businesses and affect the state’s economic climate. Sick-leave supporters said the benefit would help businesses attract and retain employees.

The House also voted 132 to 2 for a Senate bill that would increase penalties for adults who provide alcohol to underage drinkers. The bill was amended in the House and has to return to the Senate for final approval.

Busch said that Del. Sheila E. Hixson (D-Montgomery) was expected to be released from the hospital sometime Friday after she was admitted when she became ill at the State House on Thursday.