* Notarizing documents for use outside of the notary's home state. A notary public may notarize documents for use in another state if the document is accompanied by a certificate of conformity. A certificate of conformity is a statement, signed by the notary public, that the notarial act was performed in accordance with the laws of the notary's home state.
* Notarizing documents for members of the armed forces or their dependents. A notary public may notarize documents for members of the armed forces or their dependents, regardless of where the notary public is commissioned.
* Notarizing documents for use in a foreign country. A notary public may notarize documents for use in a foreign country if the document is accompanied by an apostille. An apostille is a certification, issued by the Secretary of State, that the notarial act was performed by a notary public who is duly commissioned in the United States.
In addition to these exceptions, some states have reciprocity agreements with other states that allow notaries public to perform notarial acts in each other's states. For example, New York and Connecticut have a reciprocity agreement that allows notaries public from either state to perform notarial acts in the other state.
So, to answer your question, a notary from New York can notarize documents from Connecticut if the document is accompanied by a certificate of conformity, or if the document is being notarized for a member of the armed forces or their dependents, or if the document is being notarized for use in a foreign country with an apostille.