As the subject, the correct form is "my sister and I." "My sister and I went to a party last night."

Many native English speakers will say "my sister and me," though. It's not grammatically correct, but it's very common. If you say "My sister and me went to a party last night," many people will think it sounds perfectly normal.

(Edited to add: I just realized that you're a native speaker, and I see that you also asked this same question in a different thread titled "<a href="https://www.italki.com/discussion/218395" rel="noopener noreferrer" target="_blank" style="background-color: rgb(255, 255, 255); color: rgb(0, 113, 185);">Let's exercise our language muscles</a>," so I'm guessing that you intended it to be a challenge question for non-native speakers, rather than a question for native speakers to answer. Is that right? If so, you might want to clarify that, or you'll get people like me and Tim trying to be helpful by answering. :)

If it’s used as the subject “my sister and I” is correct. “My sister and me” is used when it is the object of the sentence.

Examples.

My sister and I went to the store.

The shouted at my sister and me.

It’s easier to remember if you think of what you would say just for yourself. “Send it to me” works to remember it should be “Send it to my sister and me”. “I went to the store is correct and so is “My sister and I went to the store.”

The correct use of “my sister and me” is actually fairly rare among native English speakers. Most children start out saying “and me” for everything then you learn in school the subject form is “and I” so a lot of people switch to that for everything.

Tim and Gray's comments are very useful. Thank you!