No.

In Jain Dharma, attachment (rāga / moha) is not proved or disproved only by feeling possessive. A person may not show possessiveness outwardly and still have inner attachment.

Strict Jain answer:

• Possessiveness = one form of attachment
• But lack of possessiveness does not automatically mean no attachment

So the strictest answer is: no, not necessarily. True non-attachment means absence of inner clinging, not just absence of possessive behavior.