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A UW-Madison student was charged Wednesday with four counts of second-degree sexual assault arising from an incident last week in which another student told police she was raped.

But the lawyer for Alec R. Cook, 20, of Madison, said that his client has fully cooperated with police and that what happened early on Oct. 13 was consensual.

In addition to sexual assault, Cook was charged with three counts of misdemeanor battery, along with one count each of strangulation and false imprisonment, after the woman told police that Cook forced himself on her after they went to his apartment following a study session at a campus library.

The woman told police she had known Cook for less than two weeks, according to a criminal complaint filed in Dane County Circuit Court.

Cook, who was arrested on Monday, was released on a signature bond after appearing in court Wednesday.

According to the complaint:

The woman said she met Cook after nearly running into him while riding her bike on University Avenue. They made contact through Facebook and met four or five times after that, always in public.

On Oct. 12, the woman told police, she worked at a State Street business until 7:30 p.m., then had dinner with Cook and went with him to the College Library to study. They left the library at 11:30 p.m. and went to Cook’s apartment on North Henry Street.

She told police that she told Cook up front that she didn’t want casual sex but a longer-term relationship, and Cook said they wouldn’t do anything she didn’t feel comfortable with, the complaint states.

But at his apartment, the woman told police, light kissing became more forceful on Cook’s part, and despite telling him to stop several times, she said, he forcefully assaulted her repeatedly and would not let her leave.

After getting home, the woman told her brother by text message that she couldn’t get her phone or get to the door because Cook held her in a “death grip.” She added: “I don’t feel like I was assaulted...I don’t think. But I feel very weird.”

She told Cook by text message that night that she didn’t want to see him anymore, but he said he wanted a “second date.”

She contacted police on Sunday.

Cook’s lawyer, Chris Van Wagner, questioned why she would wait four days to call police, and said that Cook has “nothing to hide.”

“The complaint says what it says,” Van Wagner said, “but he is adamant that everything that happened was consensual.”

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Ed Treleven is the courts reporter for the Wisconsin State Journal.