The request was made Thursday in a court filing in which prosecutors also said they plan to introduce documents at trial that were found at suspect Jared Loughner's home and make references to Rep. Gabrielle Giffords, guns and bullets.
Other notebooks containing handwriting were found at the house, but no further details were provided on those documents.
The Jan. 8 attack at a Giffords political event outside a grocery store killed six people, including a 9-year-old girl, and wounded 13 others.
Investigators who searched the home of Loughner after the shooting found other handwritten notes in a safe that read "I planned ahead," ''My assassination" and "Giffords." One note said "Die, bitch," which authorities believe was a reference to Giffords.
Prosecutors said an expert will need a sample of Loughner's handwriting to determine if he wrote the documents.
Instead of agreeing to provide handwriting samples, Loughner's lawyers offered to review the documents and perhaps make an agreement about the handwriting. Prosecutors declined that request and said Loughner's handwriting samples would be taken at the federal courthouse in Tucson if permission is granted by U.S. District Larry A. Burns of San Diego.
A message left for Loughner attorney Judy Clarke wasn't immediately returned.
State and federal prosecutors also announced an agreement Friday that Loughner will be tried first in federal court before any prosecution begins on state charges.
Pima County Attorney Barbara LaWall and Dennis Burke, the U.S. attorney for Arizona, said federal law requires state prosecutions to be suspended while a federal case is pending.
Loughner pleaded not guilty to federal charges of trying to assassinate Giffords and kill two of her aides. The indictment specifying those charges superseded an earlier federal complaint that also charged him with murder for the deaths of U.S. District Judge John Roll and Giffords aide Gabe Zimmerman.
Another indictment is expected to restore those murder charges.
Loughner also will likely face state charges in the attack.
Loughner's next court hearing is set for March 9.