For the first months of the reign relations with the senate went well. A proposal was made that Gaius should immediately become consul, replacing one of the current magistrates. He rejected the move and took the consulship in the middle of the year. Even then, he quickly resigned so that the designated consul, in whose place he stood, should not be deprived of the honour.

Caligula (Commons)
He released those imprisoned by Tiberius and publicly burnt the papers relating to the trials of his mother and brothers so that there would no recriminations. He made a speech to the senate in which he promised to follow their lead and expressed himself as their ward. So pleased were the senators that they they insisted that the event by celebrated by the speech being read out annually. He abolished the crime of maiestas which had been used to terrorise the senators under Tiberius (Dio, 59.6). Everything was done to draw a conclusion to the terrors of Tiberius and establish a fresh start in imperial-senatorial relations.
The same policy was continued into 38. Under the new consuls, financial accounts were published, providing the necessary information for the senators to make a substantial contribution to the running of the state (Dio, 59.9). Election to the magistracies had been put in the hands of the senators by Tiberius. It was now returned to the people. Although this might seem like a reduction of senatorial power, it was a restoration of the Republican system and provided the senators with at least some popular mandate and legitimacy.
But already there had been signs of a different policy. Marcus Silanus had been persuaded to kill himself. The young Tiberius Gemellus was killed soon after Gaius’ illness, perhaps some had rallied to the young prince when Gaius seemed to be failing. Macro and his wife Ennia followed (Dio, 59.8-9). Gaius had quickly rid himself of the leading figures of late Tiberian years, the men who had guided his accession. It is difficult not to relate the exile of Calpurnius Piso to the change of policy. Piso was a prominent individual who was humiliated when Gaius carried off his wife Cornelia Orestilla on their wedding day. His later exile suggests a continuing distrust and hostility.
Other deaths are left by our sources without detail. Gaius returned to the deaths of his mother and brothers and removed those he could claim were responsible (Dio, 59.10) and the chronology in the accounts is obscure. The papers supposedly burnt in the amnesty of AD 37 mysteriously reappeared and the law of maiestas was restored (Dio, 59.16). Charges against senators are sometimes listed, but mostly these seem illustrative, merely demonstrating the ridiculousness of the allegations, and there is a suspicion that Gaius was after money primarily (Dio, 59.18-19).
By 39, relations with the senate as a whole were growing worse. The consuls were removed from office (Dio, 59.20) and the experiment with popular elections was shelved. Gaius went on campaign in Gaul, where he supposedly uncovered the conspiracy of Gaetulicus and exiled his sisters and killed Lepidus (Dio, 59.23). The senate responded with honours as if for a victory, but Gaius treated the proferred honours with contempt. By AD 40, the senate was not meeting. The designated consul had died and Gaius was away. The praetors did not dare to convoke a meeting. On his return from Gaul, the senators were at a loss as to what honours to offer: Gaius threatened to destroy the senate (Dio, 59.25; Suetonius, Gaius 49). There were further supposed conspiracies and deaths: one father was forced to watch his son be killed. Gaius announced an amnesty and claimed that only a few were left whom he hated: it was a terror tactic, since every senator must have wondered whether they were on that list. One person close to Gaius, Protogenes, met Scribonius Proculus in the senate house. Protogenes remarked that Proculus hated the emperor: the senators killed him on the spot.
Leading families were humiliated and stripped of ancestral honours (Suetonius, Gaius 35). Senators were humiliated by being made to run alongside his carriage or wait on the emperor at table (Suetonius, Gaius 26). Even the famous story about his horse Incitatus was probably a humiliation of the senate: Incitatus was invited to dinner and fed at the emperor’s table. The promise to make him consul showed what Gaius thought of those who dined with him and held the highest offices in the city (Dio, 59.14).
What do we make of this?
Was this just a psychopath having fun?
Gaius had reason to suspect and fear the senators. His policy shifted from one of honouring them and forgetting the disasters of the Tiberian period to one of crushing them. It is not clear what caused that shift. It is certainly not clear whether Gaius had an intended outcome from his extended conflict with the senators.
Might he have abolished the senate?
The senators in Rome had some administrative duties, but perhaps the senators who commanded the armies were more of a problem. What he seems to have wanted to demonstrated is their powerlessness and to present a monarchy that was absolute, its legitimacy resting only on the imperial family, and which depended on no other state organ.
He was murdered and in many ways it was remarkable that he lasted so long, but we may wonder whether his analysis of the imperial position was wrong.
Gaius Caligula Politics: Plebs Assassination