I think the police did find something at her house and are biding their time. Here is the LE chronology I put together from news reports.
She was reported missing on Sunday the 14th and early news article said "Dave Markham says when he entered Katelyn's condo, it appeared to him that she had been asleep. John Carter says there didn't appear to be any signs of a struggle at the home- her car is still out back and her keys, purse, and pet dog were in the house."
http://www.local12.com/news/local/s...g-Fairfield-Woman/Hb8WfZ0rpkuNpRRLpddC-w.cspx
It was reported the police went to the home on August 17 - "We need to preserve the items in the apartment, and basically take an inventory of the apartment," said Lt. Kevin Haddix of the Fairfield Police Department. While they still say nothing points to direct evidence of foul play, they're going through the process of piecing her belongings together, making sure nothing else is missing.
http://www.fox19.com/story/15286971/police-zero-in-on-missing-fairfield-womans-townhome
As the search for a missing Fairfield woman continued Wednesday, Fairfield Police Chief Mike Dickey denied reports indicating that police suspect foul play in the disappearance of Katelyn Markham. "We have no evidence of foul play. We don't know what happened,'' Dickey said. "Anything beyond that is supposition."
http://communitypress.cincinnati.co...woman?odyssey=mod|newswell|text|communities|s
Then the police returned on August 18 to secure the house and go through it and take items and said "there is no direct evidence that there was foul play involved." Police said "Basically, it's just going over the apartment more thoroughly and just looking for anything that might give us an indication of what happened to Ms. Markham and possibly where she might be - just anything we could find,". Fairfield Police Lt. Kevin Haddix said the state agency offered their help in solving the Sunday disappearance of Katelyn Markham even though "there is no direct evidence that there was foul play involved." "But as we conduct our investigation, we have to consider that possibility and react accordingly. The potential is always there," Haddix said. He would not say what was taken.
http://news.cincinnati.com/article/20110818/NEWS01/108190345/1179/WAP&template=wapart
After the search and collecting materials from the home on the 18th it is reported that, "Police now believe there was foul play in the disappearance of 22-year-old Katelyn Markham. The Butler County woman was reported missing Sunday after failing to show up for work. Police looked through her condo for clues. Her keys, purse and dog were inside."
http://www.newstalkradiowhio.com/ne...ct-foul-play-butler-county-womans-disa/nDL8w/
Since then, the police have said nothing and suspended police searches, they have increased the reward and posted requests for tips. The subsequent searches are all family and private groups.
This seems like they have an idea what happened and are biding their time. Since they have not gone public with warnings of crazed random kidnappers, this suggests they have someone in mind and that it was not a random crime. It is typical LE to let people hang themselves and make mistakes to ensure a tighter case. I am not clear if they went there on the 17th to do an inventory, then returned the 18th and removed items? It seems like they treated it as a missing person at first and then escalated it to a crime scene based on what they observed? This would suggest they know more than they are letting on and are developing some information. I am sure they are following all the online chatter putting things together.