Selection in native local breeds needs great carefulness due to the small population size and the risk of inbreeding. Furthermore, most breeds are dual-purpose, and milk and beef attitudes are antagonistic. For preservation purposes functional traits need to be considered. Focusing on the small local Rendena cattle, this study aimed to analyse the genetic correlations among milk, beef and udder health traits and the response to selection predicted under different scenarios. The study considered milk, fat and protein yields (MY), factor scores for udder volume (UV), conformation (UC) and muscularity obtained from type traits scored on primiparous cows, and performance test traits (PT) measured on young bulls at test station: average daily gain, in vivo SEUROP fleshiness, in vivo dressing percentage. Somatic cell score (SCS) was considered as a functional trait, with a possibility of restricting its genetic gain to zero. The study considered 281 497 MY test-day data collected on 16 974 cows, and data from linear type evaluation on 11 992 primiparous cows for factor scores. The PT data were recorded on 1428 young bulls, and SCS obtained from cell counts at milk recording. Bi-trait restricted maximum likelihood animal model analyses were performed to assess genetic parameters. Heritability varied from 0.157 (fat) to 0.442 (dressing percentage). Udder volume and MY resulted positively genetically correlated (average correlation 0.427), whereas the low-negative genetic correlation between MY and UC (-0.141) suggested a negative impact of milk gain on udder form. Beef traits of factor muscularity and PT showed medium-high favourable genetic correlations (from 0.357 to 0.984), excluding a null correlation between daily gain and muscularity. The genetic correlation MY v. muscularity was unfavourable (-0.328 on average), whereas null correlations were found in MY v. PT, apart from fat v. dressing percentage (-0.151). Somatic cell score showed low unfavourable correlations with protein (0.111) and UV (0.092), and favourable correlations with UC (-0.193). Response to selection in different scenarios indicated a good balanced gain for milk and beef when standardized economic weights of 0.66 and 0.34 are given to the two attitudes, and SCS genetic gain is restricted. Current genetic trends (MY and PT increasing, but muscularity lessening) reflect a stronger selection for milk, suggesting a slight progressive change towards a milk conformation. Aiming to preserve the dual-purpose characteristics of a breed, proper breeding policies taking into account the genetic relationships among traits and including functional traits should be applied in local dual-purpose populations.