With regard to third person singular pronouns with genitive function, standard Danish (and Scandinavian languages in general) distinguishes between pronouns co-referring with the gram­matical subject of their clause (i.e. pronouns used reflexively), and pronouns not co-referring with the subject. When the pronoun is co-referential with the subject, the possessive pronoun form sin (reflexive form) is chosen, when it is not, a (non-reflexive) genitive form of a personal pronoun is chosen (i.e. the Danish equivalents of his, her, ones and its).
In spoken Danish (as well as in varieties of Swedish and Norwegian), however, the use of re­flexive forms varies considerably, and non-reflexive forms are often uses in reflexive contexts:
han havde hundredhalvtreds myggestik på hans venstre side af kroppen (std. Danish: sin)
he had hundred and fifty mosquito bites on his left side of the-body
The norms regarding reflexively used pronouns are explicitly taught in the educational system and deviation from it is diligently corrected by many Danish teachers, at least as far as written lan­guage is concerned. When it comes to the spoken language, there has probably always been a great deal of variation, and none of the traditional dialects of Danish have norms with regard to reflex­ively used pronouns which are exactly like the prescribed norm of standard Danish. First and fore­most, the dialects of the western part of the country (the Jutland peninsula) have a less widespread use of reflexive forms (Jul Nielsen 1986).
The paper presents the results of a large scale survey of reflexively used pronouns in contempo­rary spoken Danish. The data material comprises recordings with 261 different speakers recorded in the period 1978-2010 (a large proportion of these have been recorded twice within this period) from four localities in Denmark. All reflexively used pronouns have been analysed using mixed effects models in order to uncover linguistic, social and geo-spatial factors constraining the use of reflexive vs. non-reflexive forms.
The results indicate that there is an ongoing change in the eastern part of Denmark (most pro­nounced in the capital Copenhagen) in which non-reflexive forms are gaining ground. The change is thus in the direction away from the prescribed standard. The paper argues that the development may be seen as a relaxation of the standard norm and a revalorization of formerly low status speech. This may explain why the standardization which in most other respects characterises the Danish speech community (e.g. Maegaard et al. 2013) seems to have stopped in Jutland with respect to re­flexive pronouns, as the traditional language use here resembles a radical version of the modern Copenhagen language use.

References:
Jul Nielsen, B. (1986): Om pronominet sin i jysk. Danske Folkemål 28: 41-100.
Maegaard, M.; T. J. Jensen; T. Kristiansen & J. N. Jørgensen (2013): Diffusion of language change: accommodation to a moving target. Journal of Sociolinguistics 17 1: 3-36.