The gunman was identified Monday as Matthew Murray, 24, who was home-schooled in what a friend said was a deeply religious Christian household. Murray's father is a neurologist and a leading multiple-sclerosis researcher.
Five people - including Murray - were killed, and five others wounded Sunday in the two eruptions of violence 12 hours and 65 miles (105 kilometers) apart.
The first attack took place at Youth With a Mission, a training center for missionaries in the Denver suburb of Arvada; the other occurred at the New Life Church in Colorado Springs, where Murray was shot by a security guard, though investigators said he may have died from a self-inflicted gunshot wound.
"Through both investigations it has been determined that most likely the suspect in both shootings are one in the same," police said in court papers Monday.
Colorado Springs police said the "common denominator in both locations" was Youth With a Mission. The training center maintains an office at the 10,000-member church.
"It appears that the suspect had been kicked out of the program three years prior and during the past few weeks had sent different forms of hate mail to the program and-or its director," police said.
Murray's relatives said they were grief-stricken and baffled.
"Our family cannot express the magnitude of our grief for the victims and families of this tragedy. On behalf of our family, and our son, we ask for forgiveness. We cannot understand why this has happened," they said in a statement read by the gunman's uncle, Phil Abeyta, who fought back tears.
In a statement, the training center said health problems kept Murray from finishing the program but elaborated little. Murray did not complete the lecture phase or a field assignment as part of a 12-week program, Youth With a Mission said.
Police gave no immediate details on the hate mail. And the training center said that Murray left in 2002 - five years ago, not three - and that no one there can recall any visits or other communication from him since then.
Earlier Monday, a law enforcement official who spoke on condition of anonymity because he was not authorized to speak publicly, said it appeared Murray "hated Christians."
Investigators have not said whether Murray singled out his victims. But the two people killed at the church - sisters Stephanie and Rachael Works, ages 18 and 16 - frequented the training center, their uncle Mark Schaepe of Lincoln , Nebraska, told The Gazette of Colorado Springs.
The two people killed at the missionary center were identified as Tiffany Johnson, 26, and Philip Crouse, 24.
Authorities searched the Murray house on a quiet street in Englewood on Monday for guns, ammunition and computers. No one was home when a reporter visited the split-level brick home early Monday. Murray 's father, Ronald S. Murray, is chief executive of the Rocky Mountain Multiple Sclerosis Center in Englewood.
Matthew Murray lived there along with a brother, Christopher, 21, a student at Oral Roberts University in Tulsa, Oklahoma. In a search warrant affidavit, investigators said Matthew Murray attended a home-based computer school and had worked at his computer for three to five hours a day for the past two years.
Police said Murray's only previous brush with the law was a traffic ticket earlier this year.
The gunman opened fire at 12:30 a.m. at Youth With a Mission. Witnesses said he asked to spend the night there and opened fire with a handgun when he was turned down. They described him as a young man, perhaps 20, in a dark jacket and cap.
Later, at New Life Church, a gunman wearing a trench coat and carrying a high-powered rifle opened fire in the parking lot and later walked into the church as a service was letting out.
Jeanne Assam, a church member who volunteers as a security guard, shot Murray, who was found with a rifle and two handguns, police said.
Assam said she believes God gave her the strength to confront Murray, keeping her calm and focused.
"It seemed like it was me, the gunman and God," she said at a news conference.
New Life Church's senior pastor, the Rev. Brady Boyd, credited her with preventing more bloodshed.
"There could have been a great loss of life yesterday, and she probably saved over 100 lives."
Boyd said the gunman had a lot of ammunition and estimated that 40 rounds had been fired inside the church, leaving what looked like a "war scene."
About 7,000 people were in and around the church the time of the shooting, Boyd said. Security had been beefed up after the shootings hours earlier in Arvada , he said. The church had a total of 15 to 20 volunteer security officers inside at the time of the attack, he said.
New Life, with a largely upper middle-class membership, was founded by the Rev. Ted Haggard, who was dismissed last year after a former male prostitute alleged a relationship with him. Haggard admitted committing unspecified "sexual immorality."
Youth With a Mission was started in 1960 and has 1,100 locations with 16,000 full-time staff, said Darv Smith, director of a Youth With a Mission center in Boulder.