The International Agency for Research on Cancer (IARC) is an agency of the World Health Organisation. Its Unit of Carcinogen Identification and Evaluation has, since 1972, periodically published Monographs which assess the evidence that various agents are carcinogenic and classify the agents accordingly. In June 2001, a Working Group met to consider static and extremely-low-frequency electric and magnetic fields. The key decision was to classify power-frequency magnetic fields as “possibly carcinogenic”. But they also classified static fields, both electric and magnetic, one category lower, "unclassifiable".
The complete results have been published as Monograph number 80. More on the scheme IARC use for these classifications.
The parts of their overall evaluation relevant to static fields are:
...There is inadequate evidence in humans for the carcinogenicity of static electric or magnetic fields and extremely low-frequency electric fields.
...No data relevant to the carcinogenicity of static electric or magnetic fields and extremely low-frequency electric fields in experimental animals were available.
...Static electric and magnetic fields and extremely low-frequency electric fields are not classifiable as to their carcinogenicity to humans (Group 3)."