The most likely genotypes of the parents are hetero_zygous (Tt) and homo_zygous recessive (tt). It is only this combination that you can produce close to a 50/50 ratio between the dominant and recessive phenotypes.
A cross between two hetero_zygous parents will produce a phenotypic ratio of 3:1, with the dominant phenotype winning over 75% of the time.
A cross between a homo_zygous dominant parent with any other parent will produce all offspring with the dominant phenotype.
A cross between two homo_zygous recessive parents will produce all offspring with the recessive phenotype.
So only a cross between a hetero_zygous and a homo_zygous recessive parent will produce a ratio close to that of the question.