The handgun that fired a single bullet into Kate Steinle on San Francisco’s Pier 14 would not have discharged without a pull of the trigger, a criminologist testified Tuesday as prosecutors sought to prove the killing was no accident.

Gerald Andrew Smith, a supervising criminologist at the San Francisco Police Department crime lab, took the stand on the sixth day of the trial of Jose Ines Garcia Zarate, whose release by San Francisco authorities 2½ months before the shooting despite a federal request to hold him for deportation ignited a political firestorm.

“I found no mechanical malfunctions or issues with the firearm,” Smith said of the .40-caliber Sig Sauer pistol, which was fished out of the bay by a dive team after the July 1, 2015, shooting. “The trigger will have to be pulled in order for the gun to operate.”

Steinle had been strolling with her father when she was shot, and the prosecution contends Garcia Zarate pulled the trigger and fired toward Steinle, an intentional act showing the malice needed for a second-degree murder conviction.

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Defense attorneys say prosecutors can’t prove that Garcia Zarate, 45, intentionally squeezed the trigger. They contend that the gun fired after the homeless undocumented immigrant found it bundled in a T-shirt or cloth under a seat at the pier. The defense cites as evidence that the bullet skipped off concrete before hitting Steinle in the back.

The handgun had been stolen from an off-duty U.S. Bureau of Land Management ranger’s parked car on the Embarcadero four days before the shooting. No one has been arrested in the burglary, and Superior Court Judge Samuel Feng told jurors Tuesday they should not speculate about whether Garcia Zarate had committed the theft.

Smith testified that when he received the gun for examination, it had one round in the chamber and six in the magazine. That was consistent with the earlier testimony of the Land Management ranger, John Woychowski Jr. He testified that he always kept this gun, his secondary firearm, fully loaded, with one round in the chamber and seven in the magazine.

The gun was in single-action mode, Smith said, typical for a gun that had been fired. A gun in double-action mode requires extra pressure on the trigger to cock the hammer and fire the bullet, while a gun in single-action mode already has the hammer cocked and requires less trigger pressure.

This is a key point of contention in the case. If the gun was in single-action mode at the time of the shooting, said defense attorney Matt Gonzalez of the city public defender’s office, it’s more likely that Garcia Zarate could have pulled the trigger accidentally when he grabbed the bundle or unwrapped the cloth around the gun. Prosecutors dispute evidence of an accidental shot.

Woychowski testified that he always left the pistol in double-action mode, but he also said the gun was typically in single-action mode when he loaded it, and couldn’t definitively say he remembered putting it back in double-action mode before it was stolen.

In any event, Gonzalez said, no one knows what happened to the gun in the four days between the burglary and the shooting.

Smith testified that he measured the trigger pull of the gun — the force required for the hammer to fall — and found that the gun required a pull of 4.8 to 5.5 pounds in single-action mode and 9 to 9.8 pounds in double-action mode. Smith said the measurements were within the manufacturer’s standards.

In his cross-examination of Smith, Gonzalez established that the weapon did not have external safety mechanisms that keep a gun from firing. The defense attorney has contended that some law enforcement officers prefer Sig Sauer pistols for this reason, that they can be fired quickly, but that even police trained in the gun’s use have a record of accidental discharges.

Smith said Sig Sauers have internal safety mechanisms that prevent the weapon from discharging if someone drops it.

“Sig Sauers are very well-made firearms,” he testified. “Law enforcement and military use them. They have a great reputation.”

Outside court, Gonzalez said he felt it was misleading to call those internal mechanisms “safety features.”

“It would be as if I said that the door to my home did not have a dead bolt on it, but you have to turn the knob to get in and that’s the safety feature,” he said. “They’re not safety features in my opinion. A safety feature is something that when you pull a trigger, the gun does not fire.”

He said he’s asking the judge to allow jurors to pull the gun’s trigger in both single-action and double-action mode to feel the difference.

“It would put to rest this debate that’s going on about whether or not it’s hard to do,” Gonzalez said.

The Steinle family is suing the Bureau of Land Management. Following Steinle’s death, legislators pushed to tighten requirements for securing weapons, especially in unattended cars, for gun owners and law enforcement officers.

Steinle’s death sparked critics to push against San Francisco’s immigration sanctuary policies. Garcia Zarate had been on track for a sixth deportation when the Sheriff’s Department, relying on those policies, released him from jail despite a federal request to hold him for deportation. He had ended up in the city on a transfer from federal custody in March 2015, thanks to old allegations — soon dismissed — that he fled marijuana charges in 1995.

Vivian Ho is a San Francisco Chronicle staff writer. Email: vho@sfchronicle.com

Twitter: @VivianHo