Legal rights refer to rights in accordance with the law,legal rights are based on a societies customs and laws, with the ubiquitous nature of law in mind it could be assumed legal rights exist in every modern society.An example of a legal right is the right to vote, in any society voting is considered a delicate issue as it involves the enthronement of a new leader charged with the responsibility of pleasing his people,different factors influence the voting choice of people some which may include the ability of the candidate to appeal to their emotions , with this example it's clear that a "conscious robot" will be incapable of participating in the electoral process making "it" unqualified to have such rights.
Another example would be the right to life, in most modern societies the right to life is embedded into the constitution making it a legal right, in the case of a "conscious robot " I'll assume "conscious" indicates it's intelligence which is not an indication of the existence of life, regardless of the robot being capable of making decisions and mimicking emotions, it would be illogical to grant it the right to life simply because it is not alive biologically nor emotionally , instead it should be protected by property rights.
Basically what I'm saying is a robot no matter it's mental capabilities should not and cannot be granted the same legal rights as humans simply because it is a lower "life" form.