All the political snarls in a plan to fund a new shock-trauma center in Baltimore were removed yesterday in a letter designed to let all legislative combatants claim victory.

The legislature has agreed to appropriate $21 million this year for a new five-story, 72-bed facility. Legislative leaders also have agreed to push for an additional $10 million grant next year to finish the project.

Legislative leaders originally announced the deal exactly one week ago. But hitches developed when the chairman of the House Appropriations Committee, Del. Clayton Mitchell (D-Kent), said he could not go along with the pledge for $10 million in construction funds next year.

Mitchell and his committee initially wanted the second chunk of money in 1986 to be limited to equipment purchases. That would have left the University of Maryland Medical System Corp. without enough state funds to build the $28 million shock-trauma unit.

Gov. Harry Hughes, in an effort to undo the political snarls, agreed to send his own letter to the hospital, declaring both his support and that of legislative leaders for additional construction money next year.

In the letter, which was mailed yesterday, Hughes pledged both his support, and that of legislative leaders, for an "unrestricted" $10 million grant next year.

To appease the House Appropriations Committee, the letter continued, "You should be aware of the grave reservations which the fiscal leadership of the House of Delegates attaches to this project.

"House members feel strongly that every effort should be expended in the design, construction and operation of this project to ensure that, to the extent possible, University Hospital and Shock Trauma staff share support services, staff and other resources to the benefit of patients at both institutions.

"Duplicative services and staff that are not dictated by the needs of patients should be avoided."