The Catholic Church, which does generally claim to follow the Bible, should follow the commands in the New Testament that specifically relate to tax evasion. Examples that weren't explicitly previously mentioned would be Romans 13:1-7 and Matthew 21:15-22.
1 Let everyone be subject to the governing authorities, for there is no authority except that which God has established. The authorities that exist have been established by God. 2 Consequently, whoever rebels against the authority is rebelling against what God has instituted, and those who do so will bring judgment on themselves. 3 For rulers hold no terror for those who do right, but for those who do wrong. Do you want to be free from fear of the one in authority? Then do what is right and you will be commended. 4 For the one in authority is God’s servant for your good. But if you do wrong, be afraid, for rulers do not bear the sword for no reason. They are God’s servants, agents of wrath to bring punishment on the wrongdoer. 5 Therefore, it is necessary to submit to the authorities, not only because of possible punishment but also as a matter of conscience.
6 This is also why you pay taxes, for the authorities are God’s servants, who give their full time to governing. 7 Give to everyone what you owe them: If you owe taxes, pay taxes; if revenue, then revenue; if respect, then respect; if honor, then honor.
And Matthew 21:15-22
15 Then the Pharisees went out and laid plans to trap him in his words. 16 They sent their disciples to him along with the Herodians. “Teacher,” they said, “we know that you are a man of integrity and that you teach the way of God in ?accordance with the truth. You aren’t swayed by others, because you pay no attention to who they are. 17 Tell us then, what is your opinion? Is it right to pay the imperial tax[a] to Caesar or not?”
18 But Jesus, knowing their evil intent, said, “You hypocrites, why are you trying to trap me? 19 Show me the coin used for paying the tax.” They brought him a denarius, 20 and he asked them, “Whose image is this? And whose inscription?”
21 “Caesar’s,” they replied.
Then he said to them, “So give back to Caesar what is Caesar’s, and to God what is God’s.”
22 When they heard this, they were amazed. So they left him and went away.