連絡してね。
to ask for information about something
連絡して下さい。
to sever the connection―cut off the communication―(between the two)
to establish a connection (with something)
そのつど連絡してくれ
I will get back to you soon.
連絡してくださいね。
to sever the connection (between the two―with the other)―cut off the communication (between the two―with the other)
I will let you know after making inquiries.
to establish a connection (between the two―with the other)