Does the federal refund be deposit first and then the state refund and if so how long does it take for both to be deposited?

[Bsch4477]

The two tax systems are entirely independent so refund times depend upon their staffing, policies and often what credits and other information is reported. 

[mesquitebean]

Here's how you can monitor the status of the refunds:

First, if you efiled, go to the Tax Home and check the efile status to be sure the returns were successfully efiled.   What is displayed at the Tax Home--accepted, rejected, printed, started, or what?

If accepted, what is showing for the Federal refund at the IRS "Where's My Refund" tool?

https://www.irs.gov/refunds

If you filed a state return, and if the efile was accepted, or if you mailed the state return, you can find your state's lookup tool here:

FAQ:  How do I track my state refund?

https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-refund/track-state-refund/L3jgO8PGs_...