What may have been a team of burglars with their eyes on a heavenly bounty busted into a Lower Pacific Heights church Tuesday night and stole a refrigerator-sized safe whose contents are invaluable. But the loot might not be what the thieves were praying for.

The safe contained thousands of dollars worth of store gift cards, according to officials of St. Dominic’s Catholic Church, but the real value was in 20 leather-bound books that contained records from religious ceremonies — baptisms, marriages, funerals — dating to 1873 when the church was founded.

“Money is replaceable in a sense, but what isn’t are the records of people who were married here or baptized here,” said the Rev. Christopher Wetzel.

The sacramental records are valuable not just as historical documents but because some of them are required for parishioners hoping to get married, get a marriage annulled or for other religious purposes.

St. Dominic’s is offering a $10,000 reward for the bound documents. Anyone with information may contact the church by email at michael@stdominics.org or call 415-567-7824.

A church worker discovered a broken window at about 7:30 a.m. and noticed the safe missing from the church’s priory, a three-story office and residential building behind the church in the 2300 block of Bush Street near Steiner Street. The burglars — Wetzel said he thinks it would have taken at least three people to carry the safe away — left behind evidence including a hand truck and scratches on the floors.

San Francisco police officers and evidence technicians visited the crime scene and began an investigation of the burglary Wednesday morning, Officer Robert Rueca confirmed. No one has been arrested or identified as a suspect in the case, he said.

Wetzel said the safe contained about $9,000 in gift cards from retailers like Safeway and Target that were given out to help people in need. He suspects the thieves expected to find the safe filled with thousands of dollars in cash from the church’s collections at Sunday Masses. But that money was already in a bank.

“When they open the safe — if they can open it — they will be surprised at the contents,” he said.

Ken Dunckel, a professional and legitimate safecracker, expects that whoever stole the safe will be able to get it open, though it may take them a long time and a lot of effort.

“If they had the wherewithal to haul it out, they’ll get it open somehow,” he said. “They’ll hack away at it until it opens and then they’ll dump it somewhere.”

While safe heists may be relatively common in the movies, they’re not as popular in real life — or than they used to be when gangs of burglars would steal safes and take them elsewhere to bust them open, Dunckel and Rueca agreed.

Wetzel hopes that if the safe-stealers have guilty consciences or dump their leather-bound loot, it will get returned to St. Dominic’s.

“We would very much hope to get it back,” he said. “We hope someone hears about the reward and brings it back. We’d very much like to pay out that reward money.”

Michael Cabanatuan is a San Francisco Chronicle staff writer. Email: mcabanatuan@sfchronicle.com Twitter: @ctuan