[anrakushi]

ずに is essentially ないで in situations where ないで retains it's meaning of 'and' it is apparently considered for formal speech and used in written japanese but I have seen/heard it used quite a bit while in Japan. i'm sure MMM or someone will pop in and confirm this. you can basically think of it as without doing 'verb', do/did this.

an example on a non-past use of it:
辞典を使わずに読んで下さい - please read without using a dictionary.

an action must follow ずに so the following is not acceptable:
電話せずに欲しい

also に can be omitted.