Towards the middle of Nedarim 65b, the gemara hypothesizes about a conversation between the man who swears that he will not benefit his neighbor and Beis Din who try to create an opening by reminding him that the Torah has commandments which include not to take revenge, not to hate one's neighbor and to give charity to the poor.
As part of the conversation, the gemara theorizes that the man could say - its not my obligation to support my neighbor - I give to the community collection and they then can support the poor of my town. The gemara then responds - not everyone goes to the gabbai (tzedakah). Rashi explains that the gemara means to say that a person may first go to a relative or neighbor for assistance before seeking help from the gabbai.
The sefer Shearim Hamitzuyanim B'Halacha quotes the Be'er Golah who explains that this gemara is the source for the rule that if a person wants to give charity, the poor of his family should take priority. He also quotes the Sifri in Re'eh on Devarim 15-6 from which we learn that ones family comes first for support, followed by the poor of one's city.
He closes the thought by exploring the concept that although the gabbaim now need to investigate to see whether the person seeking help really requires assistance, a family member knows when his family needs help and therefore the obligation falls on them to help before the poor man goes to the gabbai.