How long does it usually take for Montana state return to be sent?

Federal and state refunds come from completely separate entities,  There is no rule as to which one will come first or how much time there will be between their arrivals.

 

STATE RETURN

Make sure your state return was accepted:  https://turbotax.intuit.com/tax-tools/efile-status-lookup/

 

To track your state refund:    

https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund

 

https://ttlc.intuit.com/community/state-taxes/help/how-do-i-contact-my-state-department-of-revenue/00/25573

In New Jersey the NJ taxation website tells you what to expect after filing a tax return.

I would suspect Montana does the same.