Refinance (Cash Out) for Financing

[Vedran Sehovic]

Hello All

I have concrete issue at hand. I am looking to invest into a rental property (or multiple) and looking into financing options.

I have 46k in savings and I also have the option of refinancing my current home and get 85k out.
I'm looking at 2 properties; one is 150k close to where I live and it rents out for $1450/month and other is 108k in another market (3 hours from me, it would involve a property manager) and it rents for $1100/month. 

I could finance either property by not touching my current mortgage, using only my savings for down payment,  or I could refinance my current property and purchase 108k property outright. Once I do refinancing and get the cash, can I use that cash as down payment for both properties? Will the banks allow that?

Any advice is appreciated, been trying to do this for a while and it looks like it's finally happening.