Hello Miguelbernardo, what you have is the 1917/30 Model helmet. The DCT stood for "Defenca Civil Territorial", part of the Portuguese Legion. These helmets started off as WW1 British made helmets, then in 1930, they were refurbished/reissued and used until 1939, when a new model 1940 was introduced, however they were still in use for some time by the DCT and other auxiliary organizations. The green cross stood for the Cross of Aviz, used by the Legião Portuguesa or Portuguese Legion, which started in 1936, and was dissolved in the 1970's.
The legion had three tiers: Escalão das Actividade Militares, 18-45 years old, Escalão Privativo da DCT, 45 years and older, and Escalão de Serviços Moderados, used for members over the age of 60.