"We are not in the position to rule anything out at this point," Colorado Springs police Sgt. Steve Noblitt told AOL News.
The investigation into the case was launched late Monday afternoon, after 43-year-old Tommy Ogden returned home from work to discover his wife, 38-year-old Rene Ogden, dead inside their home. Authorities arrived on the scene and discovered the bodies of the twins, Chase and Olivia Ogden, in a separate area of the home, police said.
According to Noblitt, the victims' bodies showed signs of "obvious trauma," but he declined to elaborate.
"[They are] definitely suspicious deaths," Noblitt said. "Whether or not the coroner will make the decision [that] they are homicides [is yet to be seen], but ... they are being investigated as such."
Police interviewed Tommy Ogden on Tuesday and released him. He is reportedly cooperating with investigators. No arrests have been made, and Noblitt said that it is too soon to say whether his department is considering anyone a suspect or person of interest in the case.
"The autopsy will probably be done today or the next day, so we don't have autopsy results yet," Noblitt said. "So, there is no arrest in the case [and] we are not [in] a position where we can make any declarations or rule anything in or out."
Tommy Ogden has not responded to e-mails from AOL News seeking his comments.
According to Denver's KUSA-TV, Tommy Ogden, a veteran of the war in Iraq, retired from the Army a sergeant first class in 2006 after 20 years of service. He is employed at the Ace Hardware Retail Service and Support Center in Colorado Springs.
A background check conducted by KUSA-TV showed that Ogden was charged with child abuse in 2001, but the El Paso County district attorney later dismissed those charges.
On Tuesday, Westword, a Denver news website, found an online account at Reunion.com that reportedly belongs to Rene Ogden. In the account profile, she discussed her life with her husband, whom she described as "wonderful," and said the couple had been married since July 1996. She also said they moved from Hawaii to Colorado Springs in May 1998.
"We have a beautiful set of twins, Chase Garrett and Olivia Brianna, who were born in 1997," reads a Reunion.com post attributed to Ogden.
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Colorado's KRDO News Channel 13, citing school officials and a family friend, reported that both of the Ogden twins had learning disabilities. Brad Ake, a Facebook friend of Rene Ogden's from Cedar Park, Texas, told a Colorado Springs newspaper that Rene seemed lonely and depressed.
"She was very sad most of the time," Ake told The Gazette. "Whenever I talked to her, chatted to her, it always seemed like she was depressed."
The same newspaper reported neighbors describing Ogden as reclusive and saying that she spent the majority of her time inside the house.
"The wife -- we've never seen her outside," neighbor Lisa Komer told the newspaper.