Verizon will hurt your credit score if you can't pay the bills or miss payments or fail to pay a bill before it's sent to collections.
However signing up for Verizon will not hurt your credit score although they do a credit check when you signup with them to determine your creditworthiness.
But when Verizon checks your credit you may see a slight drop in your credit score but as long as you continue to make payments on time and keep up with any other bills and credit the temporary drop in your credit score from Verizon checking your credit will not last too long and your credit should improve over time.
Although Verizon can hurt your credit by reporting accounts sent to collections and late payments to credit bureaus.
If you can't pay your Verizon bills on time you should arrange a payment plan with Verizon if you can do so.
Verizon does a hard credit check that appears on your credit report and can affect your score when you signup for Verizon services.
The hard credit check can slightly lower your credit score.
And if your Verizon account is sent to collections due to unpaid bills, it also negatively affects your credit score and credit report.
And if you miss a payment and or are 30 or more days late on your Verizon bill payments, Verizon can report it to the credit bureaus, which can also lower your credit score.