When you monitor with e.g. IP cameras have rules for this that you should pay close attention to:
The TV Surveillance Act
Promulgation of the law on television surveillance
The TV Surveillance Act is hereby promulgated, cf. Executive Order no. 788 of 12 August 2005, with the amendments that follow from section 4 of Act no. 542 of 8 June 2006 and section 1 of Act no. 519 of 6. June 2007.
§ 1. Private individuals may not carry out television surveillance of a street, road, square or similar area which is used for ordinary traffic.
PCS. 2. TV surveillance means continuous or regularly repeated personal surveillance by means of a remote-controlled or automatically operating television camera, camera or similar apparatus. The rules of the Act on television surveillance apply correspondingly to the installation of such a device for the purpose of surveillance.
§ 2. The provision in § 1 does not apply to:
1) Television surveillance of petrol stations, factory areas, covered shopping centers and similar areas in which business activities are conducted, if the surveillance is carried out by the person in charge of the area.
2) Television surveillance of machines where money can be withdrawn (ATMs) or can be exchanged for another currency (cash machines), or of vehicles used exclusively for the transport of money (money transport vehicles), if the surveillance is carried out by the person who has available above the vending machine or vehicle, and if the television surveillance is arranged so that it is directed only at persons who are in the immediate vicinity of the vending machine or vehicle.
3) Television surveillance carried out by banking companies, gaming casinos, hotel and restaurant companies as well as shopping centers and shops from which retail sales take place
(a) own entrances and facades; and
(b) areas which are directly adjacent to own entrances and facades and which are naturally used or can be used as an access or escape route in relation to own entrances when surveillance is clearly necessary for the purpose of combating crime.
4) Television surveillance which is not connected with the recording of images on videotape, film or the like, when it is carried out as part of surveillance of own entrances, facades, enclosures or the like.
§ 3. Private individuals who carry out television surveillance of places or premises to which there is general access, or of workplaces, must provide information about this by signage or in another clear manner.
PCS. 2 pcs. 1 does not apply to television surveillance of money transport vehicles pursuant to § 2, no. 2, and in the cases mentioned in § 2, no. 4.
§ 3 a. Public authorities that carry out television surveillance of places or premises to which there is general access, or of workplaces, must provide information about this by signage or in another clear manner.
PCS. 2 pcs. 1 does not apply to television surveillance carried out by the police or the probation service or for the purpose of protecting military installations.
§ 4. The Minister of Justice may lay down further provisions on signage, etc. according to § 3, para. 1, and § 3 a, para. 1.
§ 4 a. The Director of Police may recommend that public authorities or private individuals carry out television surveillance in accordance with applicable legislation.
§ 4 b. The Director of Police may issue orders to public authorities or private individuals who carry out or plan to initiate television surveillance in accordance with applicable legislation, with regard to the quality of recordings of images on videotape, film, etc. as well as with respect to the storage of such recordings.
§ 5. Violation of § 1, § 3, para. 1, and § 3 a, para. 1, is punishable by a fine.
PCS. Violation of orders issued pursuant to section 4 b shall be punishable by a fine.
PCS. (3) In regulations issued pursuant to section 4, a penalty of a fine may be imposed for violation of provisions in the regulations.
PCS. 4. Companies, etc. may be imposed (legal persons) criminal liability according to the rules in Chapter 5 of the Criminal Code.
PCS. 5. Search in cases of violation of the provisions of this Act may take place in accordance with the rules of the Code of Judicial Procedure on searches in cases which according to the Act may result in a custodial sentence.
§ 6. The Act enters into force on 1 July 1982.
§ 6 a. The Minister of Justice submits a report to the Folketing in the 2010-11 parliamentary year on the experiences with the provision in § 2, no. 3.
§ 7. The Act does not apply to the Faroe Islands and Greenland, but may by royal decree be brought into force for these parts of the country with the deviations that the special Faroese or Greenlandic conditions require.
Act no. 542 of 8 June 2006 amending the Penal Code, the Code of Judicial Procedure and various other laws (Strengthening efforts to combat terrorism, etc.) 1) contains the following entry into force provision:
§ 9
PCS. 1. The Act shall enter into force on the day following the executive order in the Official Gazette, cf. 2-5. § 6 applies to requests for extradition pursuant to the Council of Europe Convention on the Prevention of Terrorism, or the UN Convention on the Suppression of Nuclear Terrorism, which are submitted after the Convention in question has entered into force between Denmark and the foreign country in question.2)
PCS. 2-5. (Deleted)
Act no. 519 of 6 June 2007 amending the Act on the Prohibition of Television Surveillance, etc. and the Act on the processing of personal data (Extension of access to television surveillance and strengthening of legal protection in the processing of personal data in connection with television surveillance) 3) contains the following entry into force provision:
§ 3
The law enters into force on 1 July 2007. (see original text here)
You can read what the Danish Data Protection Agency says about TV surveillance here
You can also read more about the rules for monitoring on the Danish Data Protection Agency's website