"I don't know, but I'm trying to help you," "I can't remember," and "It's more complicated than you think" are among the responses he gives during interrogation in November 2009.
Sowell, 51, is charged with aggravated murder and other crimes in the deaths of 11 women whose bodies were found in and near his home that fall.
The prosecution Monday called police Detective Lem Griffin and finished playing the first tape of Sowell's statement. A second video, taken after Sowell was taken to jail, shows him yelling at police.
Sowell also is accused of attacking other women who survived, and some of them say police ignored or downplayed their complaints.
Vanessa Gay has testified that she told police Sowell raped her in 2008, before several of the victims vanished.
"I am so sad that it took this tragedy to draw attention to what is wrong with the system," she told The (Cleveland) Plain Dealer. "In my experience the justice system failed me. So who was I supposed to turn to?"