Deiodinase type 1 activity is expressed in the prostate of pubescent rats and is modulated by thyroid hormones, prolactin and sex hormones

researchgate.net/publication/6886822_Deiodinase_type_1_activity_is_expressed_in_the_prostate_of_pubescent_rats_and_is_modulated_by_thyroid_hormones_prolactin_and_sex_hormones

This clearly shows that Finasteride changes expression of thyroid enzymes and can cause hyper/hypothyroidism depending on what it has done to your DHT.