State law requires that suits against government agencies be filed within one year of the disputed action.
Some parents on Tuesday huddled in rooms in the Jefferson County Sheriff's Department to review files, listen to 911 tapes and look at videotapes shot by emergency workers.
Lawyer Dan Evans, representing the families of four wounded students, also filed a request for access to the materials.
One suit was filed Tuesday on behalf of victim Isaiah Shoels.
"Forgiveness is something we all are going to have to do one day. But today, it's not today," Shoels told CBS News Early Show co-anchor Jane Clayson Wednesday. "Under the circumstances, we can't really come to a closure until we really find out exactly what happened there in Columbine...There will be forgiveness, but I don't want to forgive the one part of it and the other part is not to be forgiven. But I want to know exactly who to forgive."
Many more suits were likely from parents who accuse Sheriff John Stone's department of ignoring warnings of potential violence by the killers, mishandling their response to the attack and then stonewalling information requests.
"I expect we will be filing a suit asking for damages," said James Rouse, who represents the families of five of those killed in the April 20 assault.
Teen-age gunmen Eric Harris and Dylan Klebold fatally shot 12 students and a teacher before killing themselves.
Twenty or more notices of intent to sue the sheriff, school board or Jefferson County government have been filed.
County Attorney Frank Hutfless, who represents the sheriff's department, did not respond Tuesday to written questions seeking comment.
The legal developments come as the Columbine community is bracing for Thursday's anniversary. Some have said they will attend memorial services, while others plan to leave the area.
School officials have planned a private assembly, followed by a public remembrance and evening candlelight vigil. There also will be several separate memorial services.
A group representing prominent Denver-area lawyers had asked for state or federal money to compensate victims and avoid the spectacle of a flood of lawsuits on the eve of the first anniversary. The request was rejected.
Several victims' parents have complained the sheriff's department has blocked access to files, making it impossible for them to determine whether they should sue.
Jefferson County District Judge Brook Jackson on Monday ordered the sheriff to let those parents examine the files. He later extended his order to allow access to the records to families of all the victims.
The lawsuit filed by Michael and Vonda Shoels on Tuesday alleged the sheriff's department had ignored warnings that Harris and Klebold were a theat.
The lawsuit noted that Judy and Randy Brown, whose son Brooks was a friend of the gunmen, told sheriff's deputies Harris operated a Web site that included threats of terrorism.
"It's a shame they had to file a lawsuit but it's the only way to get the truth," Judy Brown said.
"The problem is that the Littleton community did not recognize the black community," he told CBS News. "My son had a foul taste in his mouth when he came to that school."
"The law (enforcement officials) did not recognize the power of hate (in Littleton and at the high school)," Shoels said.
The Shoelses lawsuit further claims that once the attack began, SWAT teams delayed entering the building, allowing the gunmen to kill and wound even more students.
"The sheriff's department, Sheriff Stone, Lt. (Terry) Manwaring and the deputy sheriffs stood by while innocent children were shot," the lawsuit said. It does not specify a monetary amount being sought.
"We want to know what's going on, what happened there in that school," Michael Shoels told CBS News. "And we really want to know why...things didn't happen quicker than they did, you know, more spontaneous than they did."
The Shoels family moved several months ago to Texas, partly because of community opposition to the lawsuits. But Michael Shoels says it's a promise they made their son.
"Just 72 hours before the shooting Isaiah asked me and my wife 'what would we do if someone shot down all of our children?'" he said. "We don't know why he asked. We interrogated him."
Shoels said his son asked if his parents would get guns and shoot the killers.
"We told him we couldn't go do that because we would be killers just like them. We said that we would, however, fight them the right way for the rest of our lives. What else could I do now but this?"