I would suggest that usually 'connected to' is a physical connection in the sense that 'my computer is connected to a printer' and 'connected with' is usually used in the sense of 'in relationship' as in: Here are some useful grammar books connected with the topic we discussed.

Thanks for your explanation :)

Perhaps "connect with" would be used colloquially in a person-to-person context to mean "get to know", "become familiar with" or "think similar thoughts as" someone or even "become intimate" with someone. "Connect to" is more in the context of joining parts of things together to make something whole or complete.

Well, ex: •My cellphone signal is so weak here. It's hard to connect to him. ???? •A word "but" is a connector which can connect a sentence to another. ??? •He is connected with our rival company. ???? Don't know Enish hahh!

Can you give us an example sentence for each of them?