But officials in Virginia, where Muhammad is expected to return soon to await execution for killing a man in Prince William County, said they see little point in further trials.
Generally, a state that convicts someone has control over the person's movements.
"It is our belief that the Maryland prosecution provides sufficient 'insurance' to guarantee Mr. Muhammad's continued incarceration if, for some reason, the Virginia prosecution is overturned," said Kevin Hall, a spokesman for Virginia Gov. Tim Kaine.
"We spoke to prosecutors in each jurisdiction and let them know what we're doing and why. I think everyone recognizes it would be our ultimate decision. Our interest is that he pay for his crime. Juries in two different states now have rendered verdicts and in one has rendered a [death] sentence," Hall said.
Hall said no other states have sought detainer agreements - through which states exchange custody of prisoners - since Virginia agreed a year ago to let Maryland put Muhammad on trial.
If another state makes such a request, he said, it would have to be discussed.
Louisiana crimeJohn W. Sinquefield, first assistant district attorney for East Baton Rouge Parish in Louisiana, said prosecutors there are weighing their options.
Muhammad and his accomplice, Lee Boyd Malvo, are charged with the September 2002 killing of Hong Im Ballenger in Baton Rouge. She was shot in the head as she left work at the beauty supply house she managed.
"Right now, it's our intention that they would face justice here in Baton Rouge; that decision was made several years ago and will have to be re-evaluated," Sinquefield said.
The prosecutor said he expects to have conversations with officials in Virginia in coming weeks about the pros and cons of trying Muhammad and Malvo in Louisiana.
Among the drawbacks: The cost of the prosecution would be "extreme," he said.
"I may well decide to bring them both down here. ... The practicality of that will have to be reviewed," Sinquefield said.
"They killed a nice Christian lady, shot her down right here on a street in Baton Rouge."
Officials with the U.S. Attorney's Office in the District of Columbia said they have made no decision yet on trying Muhammad and Malvo for a killing there.
Ala., Prince George'sAnd prosecutors in Alabama did not respond to phone calls on whether they will seek to try Muhammad and Malvo for a killing in that state.