Short answer

• Monks/nuns: Never. For ascetics, even self‑defense is forbidden. Taking up arms is completely against the Mahāvratas.
• Lay Jains (householders): Intentionally killing is prohibited. Professions whose core duty is to hurt/kill (combat soldiering, armed policing) are strongly discouraged in both Digambar and Śvetāmbara traditions.

Why

• Ahimsa Anuvrat (the layperson’s limited vow of non‑violence) forbids intentional harm by mind, speech, or body, directly, through others, or by approval.
• Jain ethics distinguishes unavoidable day‑to‑day and livelihood harm from deliberate, planned violence. Defensive or livelihood harm is tolerated only as last resort and with utmost care and detachment; still, it binds karma. Planned/intentional killing is not allowed.

So, can a Jain join the army or police?

• Best aligned with Dharma: choose non‑violent or minimally violent roles that protect society without killing, such as medical corps, logistics, engineering, communications, cyber/security, legal/judge‑advocate, rescue/disaster relief, training, community policing without weapons, traffic, forensic, administration.
• Combat roles, encounter teams, or any duty where harming/killing is the expected outcome should be avoided.

If one is already serving or compelled

• Strict vegetarianism; avoid alcohol.
• Use non‑lethal methods wherever possible; never act with anger, hatred, or cruelty.
• Daily pratikraman, repentance, and charity to reduce karmic load.
• Prefer postings and tasks that minimize direct harm.

No major Digambar–Śvetāmbara difference exists here: both uphold that a lay Jain must avoid intentional violence; only unavoidable, minimal harm with vigilance is tolerated. Monastics may not engage in violence at all.

For a simple overview of the lay vows, including Ahimsa Anuvrat and its limits, see this explainer from JainKnowledge: