PCT TRACON Controller reported CHO Tower turning an IFR aircraft not in accordance with the Letter of Agreement resulting in the aircraft being vectored below the MVA for traffic avoidance.

Narrative

Shortly after assuming the position; Aircraft X; who was IFR conducting a practice approach to Runway 21 at CHO departed on a Tower assigned heading of 090. The scratchpad showed Z2E; indicating that the aircraft was going to conduct the RNAV Z 21 then depart to the east. The controller that I relieved later confirmed that the aircraft was issued the climb out instructions; 'fly Tower assigned heading; maintain 4;000' as required by the CHO Tower LOA (Letter of Agreement). The LOA also states that Tower must issue all IFR departures runway heading.The MVA east of CHO is 030. The Tower's issuance of the 090 heading did not comply with the MVA and put me in a position where an MVA violation had already occurred. No coordination was attempted by the Tower or I would have denied the heading as I do every time they ask; which they do frequently with IFR departures when they have a faster departure they need to get out behind them.When Aircraft X departed I noticed a 1200 code east of the field westbound indicating 030 +/- 100ft or so I issued traffic. It became apparent that Aircraft X was not going to be able the reach the MVA to be turned away from the traffic in time and they were on converging courses. I issued a traffic alert and advised Aircraft X to turn left immediately. I informed them that the MVA in that area was 030 but the traffic was at 030 so if they were able to stay at 025 it would keep them below the traffic; knowing the MVA would be 1;000ft above any actual obstructions. Because of the Tower's actions; the only option I had to avoid a collision was to turn the aircraft below the MVA and/or restrict them to an altitude below the MVA.This is not the first time this has occurred with CHO Tower; yet they still request turns for IFR departures or turn them with no coordination at all. I think they are under the impression that the scratchpad entry ending with an 'E' or 'W' authorizes them to turn an IFR below the MVA. Recommendation1. The LOA with CHO Tower needs to be updated to clearly state that practice approaches will be assigned runway heading. This should be done by the TRACON as part of the climb out instructions.2. The LOA with CHO Tower needs to be undated so that the 'W' and 'E' scratchpad entries are not entered for IFR practice approaches; only VFR.3.Both the Tower and the TRACON need to receive training that makes it clear that neither facility can turn an aircraft below the MVA. There must be PCT controllers still approving these turns or they would not be asking and I have seen the Tower launch fast departures behind slow moving departures not understanding that we cant turn them until they reach the MVA.4. A SID needs to be developed that (even if it includes climb rate requirements due to mountainous terrain) allows the Tower to assign divergent headings to subsequent departures. The LOA will need to be updated to either require verbal coordination for these headings or allow the use of the rundown list for this coordination.