Portugal has different entities that look after different aspects of the county's security and as it is confusing, so we decided to provide a brief outline of each organisation.
The Guarda Nacional Republicana, GNR.
This is the gendarmerie of Portugal. 
Members of the GNR are soldiers, who, unlike the agents of the Public Security Police (PSP), are subject to military law and organisation. The GNR is responsible for law enforcement in the countryside and small towns (large urban centers are patrolled by the PSP). They also provide a national highway patrol and fiscal guard. Additionally there are two military reserve regiments: an Infantry Regiment and a Cavalry Regiment. The GNR also has ceremonial duties and provides guards of honor.
GNR- Guarda Nacional Repúblicana: www.gnr.pt
GNR logoUseful Numbers are:
Lisbon Area
GNR de Sintra: 21 924 49 25
GNR - General Command: 21 321 70 00
Porto
GNR / BT- Brigada de Trânsito / Traffic Brigade: 22 339 96 00
Algarve
GNR Albufeira: 289 590 790
GNR Faro: 289 887 603
GNR Vilamoura: 289 381 780
GNR / Traffic: 289 598 730
Coimbra
GNR Coimbra: 239 794 300
GNR / BT - Brigada de Trânsito / Traffic Brigade: 239 794 400
Madeira
GNR Funchal: 291 214 460
Açores
GNR Ponta Delgada: 296 306 580
The Polícia de Segurança Pública
PSP (Public Security Police) is the Portuguese police force that works in large urban areas, towns and cities. Rural towns and areas are under the protection of the GNR. The PSP includes a Special Operations Group. The role of the PSP is public security, protecting of citizens under the law and maintaining the security of the Portuguese democracy. Traffic issues have traditionally fallen under the PSP and currently this is still the case so if you own a car or van and it is parked illegally they entitled to give you a ticket or fine or ask you to move on.
PSP- Policia de Segurança Pública: www.psp.pt
PSP logoUseful numbers are:
Lisbon
Lisbon Metropolitan Police Command: 21 765 42 42
PSP Trânsito / Traffic: 21 750 12 00
Porto
PSP / Oporto Metropolitan Police Command: 22 209 20 00
Algarve
PSP Faro: 289 822 022
PSP / Faro Command: 289 899 899
PSP Lagos: 282 762 930
Coimbra
PSP / Command: 239 851 300
Madeira
PSP / Command: 291208 400
PSP / Funchal Airport: 291 520 889
PSP Trânsito / Traffic: 291 208 400
Açores
PSP / Command: 296 282 022
PSP / Ponta Delgada Airport: 296 205 517
PSP Trânsito / Traffic: 296 284 327
Other Regions/Cities
PSP / Aveiro Command: 234 302 510
PSP / Beja Command: 284 313 150
PSP / Braga Command: 253 200 420
PSP / Bragança Command: 273 303 400
PSP / Castelo Branco Command: 272 340 622
PSP / Guarda Command: 271 222 022
PSP / Leiria Command: 244 859 859
PSP / Santarém Command: 243 322 022
PSP / Setúbal Command: 265 522 022
PSP / Vila Real Command: 259 330 240
Tourism Police Assistance
Lisbon - Esquadra de Turismo / Tourism Police Station: 21 342 16 23
Cascais - Esquadra de Turismo / Tourism Police Station: 21 486 39 29
Porto - Esquadra de Turismo / Tourism Police Station: 22 20818 33