Reference for Tahorot 6:6
סְפֵק רְשׁוּת הַיָּחִיד, טָמֵא, עַד שֶׁיֹּאמַר לֹא נָגַעְתִּי. סְפֵק רְשׁוּת הָרַבִּים טָהוֹר, עַד שֶׁיֹּאמַר נָגַעְתִּי. אֵיזוֹ הִיא רְשׁוּת הָרַבִּים. שְׁבִילֵי בֵית גִּלְגּוּל, וְכֵן כַּיּוֹצֵא בָהֶן, רְשׁוּת הַיָּחִיד לְשַׁבָּת, וּרְשׁוּת הָרַבִּים לַטֻּמְאָה. אָמַר רַבִּי אֶלְעָזָר, לֹא הֻזְכְּרוּ שְׁבִילֵי בֵית גִּלְגּוּל, אֶלָּא שֶׁהֵם רְשׁוּת הַיָּחִיד לְכָךְ וּלְכָךְ. הַשְּׁבִילִים הַמְפֻלָּשִׁים לְבוֹרוֹת וּלְשִׁיחִים וְלִמְעָרוֹת וּלְגִתּוֹת, רְשׁוּת הַיָּחִיד לְשַׁבָּת וּרְשׁוּת הָרַבִּים לַטֻּמְאָה:
A case of uncertainty [originating] in the private domain [regarding ones purity status] is impure until he says, "I did not touch [the impure object]." A case of uncertainty [originating] in the public domain is pure until he says, "I touched [the impurity]." Which is a public domain? The [narrow, steep and winding] streets [leading up to] <i>Beit Gilgul</i> and those [areas] similar to them are [considered] a private domain regarding [matters of carrying on] Shabbat, but a public domain regarding [matters of purity and] impurity. Rabbi Elazar says: the streets of <i>Beit Gilgul</i> were only mentioned because they are a private domain regarding both of them [i.e. both for matters of carrying on Shabbat and matters of purity]. The paths that lead to pits, cisterns, caves, and wine presses are each a private domain regarding Shabbat, but a public domain regarding impurity.