Charges of felony embezzlement against an Inglewood school board member were dismissed by Los Angeles Superior Court Judge Henry P. Nelson, who said the charges are a civil matter that could be cleared up by the school district. Caroline Coleman, 48, a three-term school board member, was accused of filing false expense reports to account for $1,200 in district funds she received to attend an educational conference in New Orleans in November, 1983. Deputy Dist. Atty. Thomas A. Gray claimed that Coleman filed for airline and registration expenses she did not incur. Coleman, who was suspended without pay from her job as a county probation officer in March, 1985, pending the outcome of the trial, said she will return to her position sometime next month. Her school board seat was unaffected.