Perhaps a connection can be made with the motif of deception and the destructive properties that creating illusions produces. Certainly, however, the deception of Polonius and Hamlet are intentional and driven by their motives of exposing enemies while the self-deception of Blanche DuBois is intended for self-protection.
The role of women might also be a connecting factor...Blanche and Ophelia may be compared through wants, desires, and how the men in their lives manipulate them.
This question belongs on the discussion board.
I'm glad that you're thinking critically and making connections, and I'm impressed that you know both plays well enough to compare them. I don't think, however, I'd make the connection you're making between these two plays. I'd love to see your reasons, though.
I can guess that the madness of Hamlet and Blanche DuBois is the connector for you. However, it could be argued that Hamlet's madness is brought on by the death of his father and the duplicity of his mother and uncle. Blanche's madness seems to be something that comes on more gradually and without outside cause.
Presumably it may be the setting of the 2 plays as a phallocentric one : Blanche has to always depend on men, even at the cost of warming many men's bed, which is de facto her desire while Gertrude has agreed to the marry his brother-in-law too quickly when this "marriage" could have only been an option rather than a necessity because even if she hadn't marry Claudius, she would have still enjoy the privilege as she would have been the king's (Hamlet's) mother. So the notion of desire enters here also.
On a broad level, we can see that they are both tragic plays; both bring follow the protagonists struggles and just as they are close to victory, they are destroyed.
Both Blanche and Hamlet pine for a golden past and lament their wretched present condition. Hamlet clings to his memories of his father; he tries to show his mother how poor and inadequate his uncle is as the present king compared to the virtues of his dead father. Blanche has vivid memories of how wonderful her old home was and belittles her present home with Stella.
In fact, one could say it is their inability to let go of their past that dooms both of them.