Telegram can access the following on your device:

Identity

• find accounts on the device
• add or remove accounts
• read your own contact card

Contacts

• read your contacts
• modify your contacts

Location

• approximate location (network-based)
• precise location (GPS and network-based)

SMS

• receive text messages (SMS)

Photos/Media/Files

• modify or delete the contents of your USB storage
• read the contents of your USB storage

Camera

• take pictures and videos

Microphone

• record audio

Wi-Fi connection information

• view Wi-Fi connections

Device ID & call information

• read phone status and identity

Other

• receive data from Internet
• read Google service configuration
• full network access
• view network connections
• prevent device from sleeping
• toggle sync on and off
• read sync settings
• create accounts and set passwords
• control vibration
• draw over other apps
• run at startup

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Last Update: 06/12/2015

Source:
https://play.google.com/store/apps/details?id=org.telegram.messenger