Lansing, Mich.—A man accused of stabbing his ex-girlfriend and kidnapping and killing her 2-year-old daughter has been charged with murder by Michigan’s attorney general.

Attorney General Dana Nessel charged Rashad Trice, 26, on Friday with 20 counts, including one count each of first-degree premeditated murder and felony murder in Wynter Cole Smith’s strangulation death. Both charges carry a mandatory life sentence without the possibility of parole.

The Lansing man faces 18 other state charges, including kidnapping, in connection with the crimes committed on July 2 and July 3, when he allegedly stabbed and sexually assaulted his ex-girlfriend in Lansing, stole her car and drove away with Ms. Smith. The child was later found strangled to death with a cellphone cord.

Mr. Trice is charged with numerous state counts accusing him of fleeing police who spotted his car in a Detroit suburb on July 3, crashing it into a police vehicle and trying to disarm an officer before he was taken into custody.

Ms. Smith, who was the subject of an Amber Alert, wasn’t in the stolen vehicle. Her body was found on July 5 in a Detroit alley nearly 100 miles from Lansing.

“We have alleged today, and our many charges reflect, a horrific and brutal crime spree from Lansing to Detroit to St. Clair Shores,” Ms. Nessel said Friday in a statement announcing the charges.

The charges include the first state murder charges filed against Mr. Trice in Ms. Smith’s death. He also faces federal charges of kidnapping and kidnapping causing death.

Mr. Trice, who is being held at the Newaygo County jail, initially faced charges in multiple different counties. But Ms. Nessel reached an agreement with county prosecutors last week to consolidate the cases in Lansing.

The single prosecution will streamline the process and make it easier for family, law enforcement and witnesses to participate in the proceedings, The Detroit News reported.