Golden's 17-year-old sister, Rebecca, a senior at the school, said she saw the victim lying on the floor surrounded by teachers, some of whom were crying. She said she didn't know what was going on at the time, and teachers directed her away from the victim.
Mello said Sanchez had a severe neck injury but did not describe the attack. He said police were looking into the reports involving the prom rejection.
"Whether or not that's rumor, or whether or not that's fact, we don't know," Mello said. "So I think it's important that no one ... speculate on these rumors. Those are things we're looking into.
"This is something that everybody wants to get to the bottom of and find out why it happened, how it happened and what can we do to make sure it doesn't happen again," he said.
Mello said town schools are very safe, despite not having metal detectors. He said police will be reviewing surveillance camera footage for evidence.
Janet Golden, Sarah and Rebecca's mother and a Milford alderman, said she rushed to the school to get her daughters. She said the stabbing most likely will result in more community discussions about school security, like those that were spurred by the mass shooting at Sandy Hook Elementary School in Newtown in December 2012.
"How can we create an environment that's safe for our children?" Janet Golden asked. "My daughter actually saw the victim lying on the floor, so I'm dealing with kids that are pretty traumatized now. I can't believe this is happening in our town. It's frightening."
A moment of silence was observed in Connecticut's House of Representatives for Sanchez, and students and town officials say her death was devastating to the community.
"This is a terrible day here in Milford," said state Sen. Gayle Slossberg, who represents Milford.
Associated Press writer Pat Eaton-Robb in Hartford, Conn., contributed to this report.