Siman 348
Presented here for study, not as a practical ruling. The Shulchan Aruch rules by Sephardi custom, the Rema's glosses by Ashkenazi custom, and the Kitzur follows Ashkenazi custom. For a practical question, ask your rabbi.
א שׂוֹרְפִין עַל הַמְּלָכִים אוֹ עַל הַנְּשִׂיאִים (טוּר בְּשֵׁם תּוֹסֶפְתָּא), מִטָּתָן וּכְלֵי תַּשְׁמִישָׁן, אֲבָל עַל הַהֶדְיוֹטוֹת אָסוּר.
1 They burn at [the funerals] of Kings, or [ at the funerals ] of princes, their bed[s] and articles which they used, but for commoners it is forbidden [to do so].
ב הָאוֹמֵר: אַל תִּקְבְּרוּהוּ מִנְּכָסָיו, אֵין שׁוֹמְעִין לוֹ, אֶלָּא מוֹצִיאִין מִיּוֹרְשָׁיו כָּל צָרְכֵי קְבוּרָתוֹ בְּעַל כָּרְחוֹ, וְכֵן כָּל מַה שֶּׁרְגִילִין לַעֲשׂוֹת לִבְנֵי מִשְׁפַּחְתּוֹ, וַאֲפִלּוּ הָאֶבֶן שֶׁנּוֹתְנִין עַל הַקֶּבֶר; וְהוּא שֶׁיָּרְשׁוּ מָמוֹן מֵאֲבִיהֶם.
2 One who gave instructions [that when he dies] he should not be buried at the expense of his estate, is not to be obeyed, but they collect from his heirs [for] all his burial needs against their will, and likewise [for] all that is customarily done for [other] members of his family, and even [for] the stone that is placed upon his grave, provided that they inherited money from their father.
ג אֲפִלּוּ מִי שֶׁאֵין לוֹ מָמוֹן שֶׁצִּוָּה וְאָמַר: אַל תִּקְבְּרוּהוּ, אֵין שׁוֹמְעִין לוֹ.
3 Even one who has no money, who gave instructions [that when he dies] he should not be buried [in order not to become a public charge], is not to be obeyed.