This study intends to analyze a structure of Spanish infinitival clause non-subcategorized by matrix verb. Although the infinitives do not have morphologically realized agreement, they can have overt subject providing clausal interpretation apart from the matrix clause. I investigate the syntactic structure for non-subcategorized infinitival clauses with overt subject that function as adjunct or subject, comparing with subcategorized ones that function as complement. I argue that non-subcategorized infinitival clauses are projected to CP and infinitives have abstract agreement features. For this analysis, I claim that the concept of feature inheritance proposed by Chomsky(2007, 2008) is applied to infinitival clauses. T inherits agreement features from the phase head C and can probe the subject of the infinitive. Therefore, Case is closely related with phase head. On the other hand, I propose that subcategorized infinitival clauses represent TP category and they do not have relationship with C. As a result, T in subcategorized infinitival clauses do not inherit agreement feature from C and infinitives cannot have overt subject.